Sergei Novikov - List of publications#


1. Cohomology of the Steenrod algebra. Dokl. Akad. Nauk SSSR, 1959, v. 128, N 5, 893-895 (submitted 29.05.1959).

2. Some problems in the topology of manifolds connected with the theory of Thom spaces. Dokl. Akad. Nauk SSSR, 1960, v. 132, N 5, 1031-1034 (submitted 16.02.1960).

3. On embedding simply-connected manifolds in Euclidean space. Dokl. Akad. Nauk SSSR, 1961, v. 138, N 4, 775-778 (submitted 20.01.1961).

4. On the diffeomorphisms of simply-connected manifolds. Dokl. Akad. Nauk SSSR, April 1962, v. 143, N 5, 1046-1049 (submitted 09.11.1961).

5. Smooth manifolds of a general homotopy type, Intern. Cong. Math., Stockholm, 1962, section 4, 139. 6. Homotopy properties of Thom complexes. Mat. Sb. 1962, v. 57, N 4, 406-442. English translation with the author’s comments.

7. Homotopy properties of the group of diffeomorphisms of a sphere. Dokl. Akad. Nauk SSSR, 1963, v. 148, N 1, 32-35 (submitted 23.06.1962). 8. Some properties of (4k+2)-dimensional manifolds. Dokl. Akad. Nauk SSSR, 1963, v. 153, N 5, 1005-1008 (submitted 13.06.1963).

9. Differential topology, Itogi Nauki (Algebra and Topology), Inst. Nauchn. Informatsii Akad. Nauk SSSR, 1963, 134-160.

10. Homotopically equivalent smooth manifolds, I. Izv. Akad. Nauk SSSR, 1964, v 28, N 2, 365-474.

11. Foliations of codimension 1 on manifolds, Dokl. Akad. Nauk SSSR, 1964, v. 155, N 5, 1010-1013. 12. Foliations of codimension 1, Dokl. Akad. Nauk SSSR, 1964, v. 157, N 4, 788-790.

13. Smooth foliations on three-dimensional manifolds, Uspekhi Mat. Nauk, 1964, v. 19, N 6, 89-91.

14. Main trends of algebraic topology and algebraic geometry, Uspekhi Mat. Nauk, 1964, v. 19, N 6, 75-82 (with I. I. Pyatetskii-Shapiro and I. R. Shafarevich).

15. Gorki mathematical seminar on homotopic topology (June 1964), Uspekhi Mat. Nauk, 1964, v. 19, N 6, 237-238 (with M. I. Vishik and M. M. Postnikov).

16. The Topology Summer Institute, Seattle, 1963, Uspekhi Mat. Nauk, 1965, v. 20, N 1, 147-170.

17. New ideas in algebraic topology (K-theory and its applications). Uspekhi Mat. Nauk, 1965, v. 20, N 3, 41-66.

18. Homotopic and topological invariance of certain rational classes of Pontryagin. Dokl. Akad. Nauk SSSR, 1965, v. 162, N 6, 1248-1251.

19. Topological invariance of rational Pontryagin classes. Dokl. Akad. Nauk SSSR, 1965, v. 163, N2, 298-300.

20. Differentiable sphere bundles, Izv. Akad. Nauk SSSR, 1965, v. 29, N 1, 71-96.

21. Rational Pontryagin classes, Homeomorphism and homotopy type of closed manifolds I. Izv. Akad. Nauk SSSR, 1965, v. 29, N 6, 1373-1388.

22. Structures on manifolds, Proc. 4th All-Union Topology Conference (Tashkent 1963), 1965, 90-120.

23. The topology of foliations, Trudy Moskov. Mat. Obshch, 1965, v. 14, 248-278.

24. On manifolds with free Abelian fundamental group and their applications. Izv. Akad. Nauk SSSR, 1966, v. 30, N 1, 207-246. The translation has been made by AMS in 1968, s. 2, v. 71 (1968), pp. 1-42. This article also has been translated recently in the Topological Library v 2. As far as I know the work of Siebenmann mentioned in the footnote at the page 38 never has been published

25. Traces of elliptic operators on submanifolds and K-theory, Dokl. Akad. Nauk SSSR, 1966, v. 170, N 6, 1265-1268 (with B. Yu. Sternin).

26. Elliptic operators and submanifolds, Dokl. Akad. Nauk SSSR, 1966, v. 171, N 3, 525- 528 (with B. Yu. Sternin).

27. The Cartan-Serre theorem and intrinsic homology. Uspekhi Mat. Nauk, 1966, v. 21, N 5, 217-232.

28. Pontryagin classes, the fundamental group and some problems of stable algebra. Int. Mat. Congr., Moscow, Thesis, 1966, 158-159 (preprint).

29. Second topology summer school (Druskininkai, Lithuanian SSR, 17-29 June 1965), Uspekhi Mat. Nauk, 1966, v. 21, N 2, 257-258 (with A. A. Kirillow, D. B. Fuks and I. R. Shafarevich).

30. Operation rings and spectral sequences of Adams type in extraordinary cohomology theories, U-cobordisms and K-theory, Dokl. Akad. Nauk SSSR, 1967, v. 172, N 1, 33-36.

31. Methods of algebraic topology from the point of view of cobordism theory. Izv. Akad. Nauk SSSR, 1967, v. 31, N 4, 885-951.

32. Adams operators and fixed points. Izv. Akad. Nauk SSSR, 1968, v. 32, N 6, 1245-1263.

33. Homotopic and differential topology history of mathematics in the Fatherland, Naukova Dumka, Kiev, 1968, v. 3, 511-529 (with A. M. Vinogradov).

34. Pontryagin classes, the fundamental group and some problems of stable algebra, in Essays on Topology and Related Topics. (Memoires dedies a Georges de Rham), Springer, New York, 1970, 147-155.

35. Algebraic construction and properties of Hermitian analogues of K-theory over ring with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes, I. Izv. Akad. Nauk SSSR, 1970, v. 34, N2, 253-288.

36. Algebraic construction and properties of Hermitian analogues of K-theory over rings with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and the theory of characteristic classes, II. Izv. Akad. Nauk SSSR, 1970, v. 34, N 3, 475-500.

37. Analogues hermitiens de la K-theorie, Actes Congr. Intern. Math (Nice 1970), Gauthier-Villars, Paris, 1971, vol. 2, 39-45.

38. Formal groups, power systems, and Adams operators. Mat. Sb. 1971, v. 84, N 1, 81- 118 (with V. M. Buchstaber).

39. Formal groups and their role in the apparatus of algebraic topology, Uspekhi Mat. Nauk, 1971, v. 26, N 2, 131-154 (with V. M. Buchstaber and A. S. Mishchenko).

40. On some characteristics of cosmological models, Zh. Eksper. Teoret. Fiz., 1972, v. 62, N 6, 1977-1990.

41. A necessary reconstruction of mathematical education, Priroda, 1973, N 2, 57.

42. Singularities of the cosmological model of the Bianchi IX type according to the qualitative theory of differential equations, Zh. Eksper. Teoret. Fiz., 1973, v. 64, N 5, 1475-1494 (with O. I. Bogoyavlenskii).

43. A periodic problem for the Korteweg-de Vries equations, I. Funktsional Anal. i Prilozhen., 1974, v. 8, N 3, 54-66.

44. Periodic and conditionally periodic analogues of the many soliton solutions of the Korteweg-de Vries equations, Zh. Eksper. Teoret. Fiz., 1974, v. 67, N 12, 2131-2143 (with B. A. Dubrovin).

45. A periodic problem for the Korteweg-de Vries and Sturm-Liouville equations. Their connection with algebraic geometry, Dokl. Akad. Nauk SSSR, 1974, v. 219, N 3, 531- 534 (with B. A. Dubrovin).

46. Qualitative theory of homogeneous cosmological models, Trudy Sem. Petrovsk., 1975, v. 1, 7-43 (with O. I. Bogoyavlenskii).

47. The connection between the Hamiltonian formalisms of stationary and nonstationary problems, Functional Anal. Appl., 1976, v. 10, N 1, 9-13 (with O. I. Bogoyavlenskii).

48. Non-linear equations of Korteweg-de Vries type, finite zone linear operators, and Abelian varieties, Uspekhi Mat. Nauk, 1976, v. 31, N 1, 55-136 (with B. A. Dubrovin and V. B. Matveev).

49. The Schroedinger equation in a periodic field and Riemann surfaces, Dokl. Akad. Nauk SSSR, 1976, v. 229, N 1, 15-18 (with B. A. Dubrovin and I. M. Krichever).

50. Homogeneous models in general relativity theory and gas dynamics , Uspekhi Mat. Nauk, 1976, v. 31, N 5, 33-48 (with. O.I. Bogoyavlenskii).

51. Algebraic topology, Encyclopedia of Mathematics, 1977, vol. 1, 170-174.

52. Petr Konstantinovich Rashevskii (on his seventieth Birthday), Uspekhi Mat. Nauk, 1977, v. 32, N 5, 205-209 (with A. T. Fomenko).

53. Methods of algebraic geometry in contemporary mathematical physics, Math. Phys. Reviews,1978, 1-54 (with V. G. Drinfel'd, I. M. Krichever and Yu. I. Manin).

54. Problems in geometry, Moscow State University, M. 1978 (with A. S. Mishchenko, Yu. P. Solov'ev and A. T. Fomenko). 55. Holomorphic vector bundles over Riemann surfaces and the Kadomtsev-Petviashvili (KP) equation. I, Funktsional Anal. i Prilozhen, 1978, v. 12, N 4, 41-52 (with. I. M. Krichever).

56. A method of solving the periodic problem for the Korteweg-de Vries equation and a generalization of it, Proc. All-Union Conf. on partial differential equations, dedicated to I. G. Petrovskii on his seventy-fifth birthday, Moscow State University, M. 1978, 184-185.

57. Algebraic geometry and mathematical physics, Proc. Conf. on fundamental problems in mathematics and theoretical physics, dedicated to the 70th birthday of Academician N. N. Bogolyubov, Joint Institute of Nuclear Research, Dubna, 1979, 459-473.

58. Modern geometry. Methods and applications, Nauka, Moscow, 1979 (with B. A. Dubrovin and A. T. Fomenko).

59. Holomorphic fiberings and non-linear equations. Finite zone solutions of rank 2, Dokl. Akad. Nauk SSSR, 1979, v. 247, N 1, 33-37 (with I. M. Krichever).

60. Solutions to the Ginzburg-Landau equations for planar textures in superfluid He-3, Comm. Math. Phys., 1979, v. 69, 237-246 (with V. L. Golo and M. I. Monastyrskii). 61. Methods of qualitative theory of dynamics systems in general relativity theory, Non-linear waves, Nauka, Moscow, 1979, 164-176 (with O. I. Bogoyavlenskii).

62. Holomorphic bundles over algebraic curves and nonlinear equations. Uspekhi Mat. Nauk, 1980, v. 35, N 6, 47-68 (with I.M. Krichever).

63. The theory of solitons and method of the inverse problem, Nauka, Moscow, 1980 (with V. E. Zakharov, S. V. Manakov, and L. P Pitaevskii).

64. Ground states of a two-dimensional electron in a periodic magnetic field. Zh. Eksper. Teoret. Fiz., 1980, v. 79, N 3, 1006-1016 (with B. A. Dubrovin).

65. Ground states in a periodic field. Magnetic Bloch functions and vector bundles. Dokl. Akad. Nauk SSSR, 1980, v. 253, N 6, 1293-1297 (with B. A. Dubrovin).

66. A method of solving the periodic problem for the KdV equations and its generalization, in Solitons, ed R. K. Bullough and P. J. Caudrey, Topics in Current Physics 17, Springer, Berlin - New York, 1980, 325-338.

67. Linear operators and integrable Hamiltonian systems, Proc. Intern. Congr. Math. (Helsinki 1978), Helsinki, 1980.

68. Multivalued functions and functionals. An analogue of the Morse theory, Dokl. Akad. Nauk SSSR, 1981, v. 260, N 1, 31-35.

69. Periodic solutions of the Kirchhoff equations for the free motion of a rigid body in a fluid and the extended Lyusternik-Shnirel'man-Morse theory. I, Funktsional Anal. i Prilozhen., 1981, v. 15, N 3, 54-66 (with I.Shmel'tser).

70. Variational methods and periodic solutions of equations of Kirchhoff type. II, Funktsional Anal. i Prilozhen., 1981, v. 15, N 4, 37-52.

71. Bloch functions in a magnetic field and vector bundles. Typical dispersion relations and their quantum numbers, Dokl. Akad. Nauk SSSR, 1981, v. 257, N 3, 538-543.

72. Kirchhoff type equations and many-valued functions and functionals. Analogue of the Morse-Lyusternik-Shnirel'man theory and periodic orbits in a magnetic field, Report to the I. G. Petrovskii seminar, Uspekhi Mat. Nauk, 1981, v. 36, N 5, 217-219.

73. Algebraic geometry and mathematical physics, in Proc. USA-USSR Conf. ed. V. E. Zakharov and S. V. Manakov, North-Holland, Amsterdam 1981 (with I. M. Krichever).

74. The Hamiltonian formalism and a many-valued analogue of Morse theory, Uspekhi Mat. Nauk , 1982, v. 37, N 5, 3-49.

75. On Poisson brackets compatible with algebraic geometry and the Korteweg-de Vries dynamics on the set of finite-zone potentials, Dokl. Akad. Nauk SSSR, 1982, v. 266, N 3, 533-537 (with A. P. Veselov).

76. Algebro-geometric Poisson brackets for real finite-zone solutions of the sine-Gordon equation and the non-linear Schroedinger equations, Dokl. Akad. Nauk SSSR, 1982, v. 267, N 6, 1295-1300 (with B. A. Dubrovin).

77. Commuting operators of rank l>1 with periodic coefficients, Dokl. Akad. Nauk SSSR, 1982, v. 263, N 6, 1311-1314.

78. On the spectral theory of commuting operators of rank 2 with periodic coefficients, Funktsional Anal. i Prilozhen., 1982, v. 16, N 1, 25-26 (with P. G. Grinevich).

79. Topological and algebraic-geometrical methods in contemporary mathematical physics, Soviet Scientific Reviews, 1982, v. 3, 1-156 (with B. A. Dubrovin and I. M. Krichever).

80. Hamiltonian formalism of one-dimensional systems of hydrodynamic type and the Bogolyubov-Whitham averaging method, Dokl. Akad. Nauk SSSR, 1983, v. 270, N 4, 781-785 (with B. A. Dubrovin).

81. Two-dimensional Schroedinger operators in periodic fields. Current Problem in Mathematics, VINITI, 1983, v. 23, 3-22. 82. Multivalued functionals in modern mathematical physics, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur, 1983, v. 117, suppl. 2, 635-644.

83. The analytic generalized Hopf invariant. Many-valued functionals, Uspekhi Mat. Nauk, 1984, v. 39, N 5, 97-106.

84. Critical points and level surfaces of many-valued functions, Trudy Mat. Inst. Steklov, 1984, v. 166, 201-209.

85. Poisson brackets and complex tori. Trudy Mat. Inst. Steklov, 1984, v. 165, 49-61 (with A.P.Veselov).

86. Modern geometry. Methods of homology theory, Nauka, Moscow 1984 (with B. A. Dubrovin and A. T. Fomenko).

87. Periodic extremals of many-valued or not everywhere positive functionals, Dokl. Akad. Nauk SSSR, 1984, v. 274, N 1, 26-28 (with I. A. Taimanov).

88. On Poisson brackets of hydrodynamic type, Dokl. Akad. Nauk SSSR, 1984, v. 279, N 2, 294-297 (with B. A. Dubrovin). 89. Discussion with Academician S. P. Novikov, Kvant, 1984, N 10, 2-5.

90. Finite-zone two-dimensional potential Schroedinger operators. Explicit formulas and evolution equations, Dokl. Akad. Nauk SSSR, 1984, v. 279, N 1, 20-24 (with A. P. Veselov).

91. Finite-zone two-dimensional Schroedinger operators. Potential operators, Dokl. Akad. Nauk SSSR, 1984, v. 279, N 4, 784-788 (with A. P. Veselov).

92. Algebro-topological approach to reality problems Real action variables in the theory of finite-gap solutions of the sine-Gordon equation. Zap. Nauchn. Sem. LOMI, 1984, v. 133, 177-196

93. An averaging method for one-dimensional systems, in Non-linear and Turbulent Process in Physics, vol 3, Harwood Academic Publ. Chur. 1984, 1529-1540.

94. The geometry of conservative systems of hydrodynamic type. The method of averaging for field-theoretical systems. Uspekhi Mat. Nauk, 1985, v. 40, N 4, 78-89.

95. Poisson brackets of hydrodynamic type, Frobenius algebras and Lie algebras, Dokl. Akad. Nauk SSSR, 1985, v. 283, N 5, 1036-1039 (with A. A. Balinskii).

96. Algebraic topology at the Steklov Mathematical Institute of the Academy of Sciences of the USSR, Trudy Mat. Inst., Steklov, 1985, v. 169, 27-49. 97. Analytical homotopy theory. Rigidity of homotopic integrals, Dokl. Akad. Nauk SSSR, 1985, v. 283, N 5, 1088-1091.

98. Integrable systems, I. Current problem in mathematics. Fundamental directions. VINITI, 1985, v. 4, 179-284 (with B. A. Dubrovin and I. M. Krichever).

99. Two-dimensional periodic Schroedinger operators and Prym's q-functions, in Geometry Today, Internat. Conf. Rome, June 1984, Boston, 1985, 106-118 (with A. P. Veselov and I.M. Krichever).

100. Differential geometry and the averaging method for field-theoretic systems, Proc. III Internat. Symp. on Selected Problem in Statistical Mechanics (Dubna, 1984), Joint. Institute of Nuclear Research, Dubna, 1985, vol. 2, 106-118.

101. Modern geometry. Methods and applications. 2nd revised edition, Nauka, Moscow 1986 (with B. A. Dubrovin and A. T. Fomenko).

102. Bloch homology. Critical points of functions and closed I-forms, Dokl. Akad. Nauk SSSR, 1986, v. 287, N 6, 1321-1324.

103. Morse inequalities and von Neumann 1-factors, Dokl. Akad. Nauk SSSR, 1986, v. 289, N 2, 289-292 (with M.Shubin).

104. Topology I. Current problem in mathematics. Fundamental directions, VINITI, 1986, v. 12, 5-251.

105. Two-dimensional Schroedinger operators: Inverse scattering transform and evolutional equations, Phys. D18, 1986, 267-273 (with A. P. Veselov).

106. Vladimir Abramovich Rokhlin (obituary), Uspekhi Mat. Nauk, 1986, v. 41, N 3, 159-163 (with V. I. Arnol'd, D. B. Fuks, A. N. Kolmogorov, Ya. G. Sinai, A. M. Vershik, and O. Ya. Viro).

107. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad. Nauk SSSR, 1987, v. 294, N 2, 325-329 (with V. V. Avilov).

108. Elements of differential geometry and topology, Nauk, Moscow, 1987 (with A. T. Fomenko).

109. Evolution of the Whitham zone in the Korteweg-de Vries theory, Dokl. Akad. Nauk SSSR, 1987, v. 295, N 2, 345-349 (with V. V. Avilov and I. M. Krichever).

110. Algebras of Virasoro type, Riemann surfaces and structures of the theory of solitons, Funktsional. Anal. i Prilozhen., 1987, v. 21, N 2, 46-63 (with I. M. Krichever).

111. Virasoro-type algebras, Riemann surfaces and strings in Minkowski space, Funktsional. Anal. i Prilozhen., 1987, v. 21, N 4, 47-61 (with I. M. Krichever).

112. Two-dimensional Schroedinger operator and solitons: 3-dimensional integrable systems. VIII Internat. Congr. on Math. Physics, Marseille 1986, World Scientific Publ. 1987, 226-241.

113. The two-dimensional inverse scattering problem for negative energy and generalized analytic functions, I. Energy below the basis state, Funktsional. Anal. i Prilozhen., 1988, v. 22, N 1, 23-33 (with P. G. Grinevich).

114. Analytical theory of homotopy groups, in Topology and Geometry, Rochlin Seminar, Lecture Notes in Math., 1988, vol. 1346, 99-112, Springer-Verlag.

115. Algebras of Virasoro type, energy-momentum tensor and decomposition operators on Riemann surfaces, Funktsional. Anal. i Prilozhen. 1989, v. 23, N 1, 24-40 (with I. M. Krichever).

116. Hydrodynamics of the soliton lattices. Differential geometry and Hamiltonian formalism. Uspekhi Mat. Nauk, 1989, v.44, N 6, 29-98 (with B. A. Dubrovin).

117. Riemann surfaces, operator fields, strings. Analogues of the Fourier-Laurent bases, in Memorial Volume for Vadim Knizhnik, "Physics and Mathematics of Strings", eds. L. Brink, D. Friedan, A. M. Polyakov, World Scientific, Singapore, 1990, 356-388 (with I. M. Krichever).

118. On the quantization of finite-zoned potentials in connection with string theory, Funktsional. Anal. i Prilozhen., 1990, v.24, N 4, pp 43-53.

119. On the equation L,A =\eps{\cdot}1, Progress of Theor Physics, Suppliment n 102, 1990, Kyoto, Japan, pp 287-292

120. Riemann Surfaces, Operator Fields, Strings. Analogues of the Fourrier-Laurent bases. Progress of Theor Physics, Suppliment n 102, 1990, Kyoto, Japan, pp 293-300

121. Hydrodynamics of the Soliton Lattices and Differential Geometry. (Collection of the survey articles. Potsdam. 1992, edited by A. Fokas.)

122. Various doubles of the Hopf algebras. Operator algebras on the quantum groups and Complex Cobordisms, Uspekhi Math. Mauk, 1992, v. 47 iss. 5, pp. 189-190, arXiv, math-ph/0004016.

123. Action-angle Variables and Algebraic Geometry, in the volume La Mechanique Analitique de Lagrange et son heritage-II, Accademia delle Scienze di Torino Suppl, 1992, v126, n 2, pp 139- 150.

124. Integrability in Mathematics and Theoretical Physics: Solitons. The Mathematical Intelligencer, 1992, Vol. 14, N 4. Springer-Verlag, New York.

125. Role of Integrable Models in the development of Mathematics. (Mathematical Research today and tomorrow: Viewpoints of seven Fields Medallists). LNM, 1992, v 1525, Springer

126. Quasiperiodic structures in Topology, In: Topological Methods in Modern Mathematics (Dedicated to the 60th birthday of J. Milnor. Stony=Brook University, 1991). Houston, TX Publish or Perish, 1993, 223-233. 127. On the Liouville form of the Poisson bracket of Hydrodynamic type and Nonlinear WKB. Uspechi Math. Nauk - Russian Math Surveys, 1993, v. 48, n.1, pp 155-156 (with A. Maltzev).

128. Hydrodynamics of Soliton Lattices. Mathematical Physics Reviews, ed by B. Dubrovin and S. Novikov, Siviet Scientific Reviews ser C, 1993, v 9, part 4, pp 58-106 (with B. A. Dubrovin).

129. String Equation - 2. Physical Solution, Algebra and Analysis, 1994, v. 6, n 3, pp 118-140; solv-int/9501002 (with P. G. Grinevich).

130. Solitons and Geometry. Fermi lectures 1992. Scuola Norm. Sup. di Pisa, Cambridge Univ. Press, 1994.

131. The Semiclassical Electron in a Magnetic Field and Lattice. Some Problems of the Low Dimensional Periodic Topology, Geometric and Functional Analysis, 1995, v. 5, n. 2, pp. 434-444.

132. Nonselfinersecting magnetic orbits on the plane. Proof of Principle of the Overthrowing of the Cycles, Topics in Topology and Mathematical Physics, 1995, AMS Translations (2), v. 170, 59-82, arXiv, solv-int/9501006 (with P. G. Grinevich).

133. Exactly solvable periodic 2-d Schroedinger operators. Russian Math.Surveys, 1995, v 50, n. 6, pp 171-172 (with A. P. Veselov).

134. Topology-1. Encyclopedia of Mathematical Sciences, Springer Verlag, 1996, vol.12, 320 p.

135. Topological quantum characteristics observed in the investigation of conductivity in normal metals, JETP Letters, vol. 63, n10, 25 May 1996, translated by the American Institute of physics, (with A.Ya. Maltsev).

136. Algebraic properties of 2D difference operators. Russia Math Surveys, 1997, vol 52, iss 1, pp 225-226

137. Discrete Spectral Symmetries of low-dimensional differential operators and difference operators on regular lattices and two-dimensional manifolds. Russian Math. Surveys, 1997, vol 52, iss 5, pp 175-234. arXiv, math-ph/0003009 (with I. A. Dynnikov)

138. Laplace Transformations and Simplicial Connections. Russian Math Surveys, 1997, v 52, n 6, pp 157-158 (with I. A. Dynnikov)

139. Schroedinger Operators on Graphs and Topology. Russian Math Surveys, 1997, v 52, n 6, pp 177-178; math-ph/0004015.

140. Exactly solvable 2-dimensional Schroedinger opeators and Laplace Transformations, published in AMS Translations (1997), ser 2, vol 179 - Solitons, Geometry and Topology: On the Crossroads, pp 109-132 edited by V. Buchstaber and S. Novikov, (with A. P. Veselov) Appendix I (S. Novikov): Difference Analogs of the Laplace Transformations. Appendix II (S. Novikov, A. Taimanov): Difference analogs of the harmonic oscillator. ArXiv, math-ph/0003008.

141. Role of Integrable Models in the development of Mathematics In: Fields Medallist Lectures". (Eds. M. Atiyah and D. Iagolnitzer). World Scientific, Singapore Univ. Press, pp. 202-217.

142. Topological Phenomena in Normal Metals, Uspekhi Phys. Nauk, March 1998, v 168, n 3, pp 249-258=Physics-Uspekhi 41(3) 231-239; cond-mat/9709007 (with A.Ya. Maltsev).

143. Schroedinger Operators on Graphs and Symplectic Geometry, published in the Fields Institute Communications vol. 24, 1999, pp 397-413. Dedicated to the 60-th birthday of V.Arnold; math-ph/0004013.

144. Discrete Schroedinger Operators and Topology, Asian Journal of Mathematics, December 1998, vol 2, n 4, pp. 921-934 (dedicated to the 70th birthday of Mikio Sato); math-ph/9903025.

145. Discrete Lagrangian Systems on Graphs. Symplecto-Topological Properties. Uspekhi Mat. Nauk=Russian Mathematical Surveys, 1999, v 54, n 1, pp 257-258; math-ph/0004011 (with A.S.Schwarz).

146. Discrete Schrodinger Operator. Published in the volume "Trudy Steklov Math. Institute, 1999, vol 224, pp 275-290 (dedicated to the 90th birthday of L. Pontryagin)

147. The levels of quasiperiodic functions on the plane and Hamiltonian systems. Uspekhi Math Nauk=Russian Math Surveys, 1999, v 54, n 5, pp 147-148; math-ph/9909032.

148. Trivalent graphs and solitons. Uspekhi Math Nauk, 1999, v 54, n 6, pp 149-150; math-ph/0004009 (with I. Krichever). 149. Periodic and almost periodic potentials in inverse problems. Inverse problems, 1999, v.15,, p.p. R117-R141. IOP Publishing Ltd. arXiv, math-ph/0003004.

150. Holomorphic bundles and scalar difference operators. One-point constructions. Uspekhi Math Nauk=Russian Math Surveys, 2000, v 55, n 2, pp 159-161; math-ph/0004008 (with I. Krichever).

151. Holomorphic bundles and commuting difference operators. Two-point constructions. Uspekhi Math Nauk=Russia Math Surveys, 2000, v 55, n 3, pp 181-182 (with I. Krichever).

152. The algebraic aspects of the multiplications in the Complex Cobordisms. Uspekhi Math Nauk=Russian Math Surveys, 2000, v 55, n 4, pp 5-24; math.AT/0103066 (with B. Botvinnik, V. Buchstaber, S. Yuzvinski).

153. I.Classical and Modern Topology. II.Topological Phenomena in Real World Physics. published in GAFA=Geometric and Functional Analysis, 2000, Special Volume GAFA-2000, Visions in Mathematics, Birkhauser Verlag, Basel, 2000, p. 406-425; math-ph/0004012.

154. On the local systems hamiltonian in the weakly nonlocal Poisson brackets, 2000, presented for publication in the Journal Fisica D in July 2000, published in June 2001; nlin.SI/0006030 (with A.Ya.Maltsev)

155. Real finite-gap solutions to the Sine-Gordon equation; formula for the topological charge. Uspekhi Math Nauk=Russian Surveys, 2001,v.56, n.5 (with P.G.Grinevich).

156. Topological Charge of the real finite-gap periodic Sine-Gordon solutions. Communications on Pure and Applied Mathematics, 2003, v. LVI, dedicated to the memory of Juergen Moser, Wiley Periodicals Inc., arXiv, math-ph/0111039.

157. A note on the real fermionic and bosonic quadratic forms: diagonalization and topological interpretation, arXiv, math-ph/0110032.

158. On the exotic de-Rham cohomology. Perturbation Theory as a Spectral Sequence, preprint, math-ph/0201019.

159. Geometry of the triangle equation on two-manifolds. Moscow Mathematical Journal, v 3(2003), pp 419-438 (this volume is dedicated to the 65th birthday of V.Arnold)(with I. A. Dynnikov), 23 pages. arXiv, math-ph/0208041.

160.Topological Phenomena in the Real Periodic Sine-Gordon Theory, Journal of Math Physics, vol 44, n 8, August 2003, pp R3137-R3147,arXiv, math-ph/0303039, (with P.Grinevich).

161. Quasiperiodic Functions and Dynamical Systems in Quantum Solid State Physics. Bull. Braz. Math.Soc., New Series 34 (1), pp 171-210, 2003. arXiv, math-ph/0301033 (with A.Maltsev )

162. 2-dimensional Toda lattice, commuting difference operators and holomorphic vector bundles, Uspekhi Math. Nauk= Russian Math. Surveys, 2003, v.58, No. 3, pp 51-88 (with I.Krichever). ArXiv, math-ph/0308019.

163. Discrete Connections on the Triangulated Manifolds and Difference Linear Equations arXiv, math-ph/0303035. This work is published in Proceedings of Steklov Math. Inst., v 247 pp. 186-201 (2004)

164. Dynamical Systems, Topology and Conductivity in Normal Metals, Journal of Statistical Physics, April 2004, vol 115, iss 1-2, pp 31-46 (16), (revised in October 2003) arXiv, cond-mat/0304471 (with A.Maltsev).

165. Integable Systems. 1. Encyclopedia Math. Sciences, Dynamical Systems, v.4 (edited by V.Arnold and S.Novikov), second, expanded and revised edition, pp 177-332, Springer-2001 (with B.Dubrovin and I.Krichever)

166. Algebraic Topology. Modern Problems of Mathematics. (Steklov Math Institute Series, founded in 2003),pp 1-46 (in Russian) A revised version of this article is published: Topology in the XXth Century: A view from inside. Uspekhi Math. Nauk=Russian Math Surveys, vol 59 (2004). n 5

167. On the metric independent exotic homology, preprint, arXiv, math.DG/0403452 This work was published in the Proceedings (Trudy) of the Steklov Math Institute, vol. 251 (2005), pp. 202-212

168. Topology of the quasiperiodic functions on the plane and dynamical systems. Uspekhi Math. Nauk, 2005, v. 60. n 1 arXiv:math.0410464 (with I. Dynnikov)

169. Topology of foliations given by the real parts of holomorphic 1-forms. arXiv, math.GT/0501338 (v1 - 21 Jan 2005, revised - February, 10, 2005 and March 31, 2005).

170. Topology of the Generic Hamiltonian Foliations on the Riemann Surface. Math.GT/0505342. New version. This work was published in the Moscow Math. Journal (MMJ) , vol 5 (2005), n 3, dedicated to the 70th birthday of Ya.G.Sinai, pp 633-667 171. Dynamical Systems and Differential Forms. Low Dimensional Hamiltonian Systems. arXiv, math.GT/0701461. Contemporary Math., 469 (AMS), vol. Probabilistic and geometric methods in Dynamical systems (K.Burns, D.Dolgopyat,Ya.Pesin, eds.), in honor of M.Brin

172. S.Novikov, I.Taimanov. Modern Geometric Structures and Fields. Graduate Studies in Mathematics, vol 75, AMS, Providence, Road Island.

173. New discretization of complex analysis. The Euclidean and hyperbolic planes. arXiv:0809.2663

174. Four Lectures: Discretization and Integrability. Discrete Spectral Symmetries. Newton Institute for Math Sciences, Cambridge University, UK, August 8-20, 2001, Special Semester dedicated to the Completely Integrable Systems and Solitons, Fall 2001. Published in the special volume (A.V.Mikhailov, editor), Springer Verlag, 2008.

175. Lectures on Discrete Systems, University of Montreal, Canada, June 13-20, 2008, to appear in the Proceedings of Workshop on the Discrete Systems and Symmetry.

176. Singular finite-gap operators and indefinite metrics. I. arXiv:0903.3976 (March 2009, with P.Grinevich). Uspekhi Matematicheskih Nauk, 2009, v. 64, no. 4, p.p. 45√72

177. New Reductions and Nonlinear Systems for 2D Schrodinger Operators, arXiv math 1001:4300 (with P.Grinevich and A.Mironov)

178. Zero level of purely two-dimensional magnetic nonrelativistic Pauli operator for spin=1/2 particles, Theoretical and Mathematical Physics, 2010, 164:3, 1110-1127 arXiv:1004.1157 (with P.Grinevich and A.Mironov)

179. 2DSchrodinger Operator; (2+1) Evolution Systems and Their New Reductions. The 2D Burgers Hierarhy, arXiv:1005.0612 and Russian Math Surveys, 2010, v 65, n 3, p. 580-582 (English) (with P.Grinevich and A.Mironov)

180. Erratum. Theoretical and Mathematical Physics, 2011, 166:2, p. 277 (with P.Grinevich and A.Mironov)

181. On the nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator. Arxiv:1101.5678 (with P.Grinevich and A.Mironov). New extended version (19 Dec 2011) see in arXive.

182. Singular Solitons and Indefinite Metric. Arxiv:1103.2505, version 3 (with P.Grinevich). A version of this work appeared also in Doklady Academii Nauk, 2011, v 436, n 3, pp.302-305 (in Russian) and Doklady Matematiki, 2011, v. 83, n.1, pp. 56-58 (in English). New extended version (1 Jan 2012) see in arXive.

183. 2D Pauli operator in the magnetic field. Low temperature physics, 2011, v. 37, pp. 829-833 (with P.G.Grinevich and A.E.Mironov). Russian version: "Dvumernyi operator Pauli v magnitnom pole" -- Fizika nizkih temperatur, 2011, t. 37, n. 9-10, s. 1040-1045;

184. Singular Solitons and Indefinite Metric. Arxiv:1103.2505 (with P.Grinevich). A version of this work appeared also in Doklady Academii Nauk, 2011, v 436, n 3, pp.302-305 (in Russian) and Doklady Matematiki, 2011, v. 83, n.1, pp. 56-58 (in English). New extended version (1 Jan 2012) see in arXive.

185. Discrete SL2 Connections and Self-Adjoint Difference Operators on the Triangulated 2-manifold Arxiv:1207.1729 (with P.Grinevich).

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