Advertisement

Multi-Valued Functionals, One-Forms and Deformed de Rham Complex

  • D. V. Millionschikov
Part of the Biological and Medical Physics, Biomedical Engineering book series (BIOMEDICAL)

Keywords

Cohomology Class Morse Theory Morse Function Morse Inequality Dirac Monopole 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. P. Novikov, Soviet Math. Dokl. 24, 222-226, (1981)zbMATHGoogle Scholar
  2. 2.
    S. P. Novikov, Russ. Math. Surveys 37 (5), 1-56, (1982)zbMATHCrossRefADSGoogle Scholar
  3. 3.
    S. P. Novikov, Soviet Math. Dokl. 33 (5), 551-555, (1986)zbMATHGoogle Scholar
  4. 4.
    A. V. Pazhitnov, Soviet Math. Dokl. 35, 1-2, (1987)Google Scholar
  5. 5.
    E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17, 661-692, (1982)zbMATHMathSciNetGoogle Scholar
  6. 6.
    S. P. Novikov, On the exotic De-Rham cohomology. Perturbation theory as a spectral sequence, arXiv:math-ph/0201019Google Scholar
  7. 7.
    L. Alaniya, Russ. Math. Surveys 54 (5) 1019-1020 (1999)zbMATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    K. Nomizu, Ann. Math. 59, 531-538, (1954)CrossRefMathSciNetGoogle Scholar
  9. 9.
    D. V. Millionshchikov, Russ. Math. Surveys 57 (4) 813-814, (2002)zbMATHCrossRefMathSciNetADSGoogle Scholar
  10. 10.
    D. V. Millionshchikov, Math. Notes (in Russian) 77(1-2), 61-71 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    J. Dixmier, Acta Sci. Math. (Szeged), 16 (4), 226-250, (1955)MathSciNetGoogle Scholar
  12. 12.
    A. Hattori, J. Fac. Sci. Univ. Tokyo, Sect. 1, 8 (4), 289-331 (1960)zbMATHGoogle Scholar
  13. 13.
    P. A. M. Dirac, Phys. Rev. 74, 817, (1948)zbMATHCrossRefMathSciNetADSGoogle Scholar
  14. 14.
    Y. Aharonov, D. Bohm, Phys. Rev. 115(3) 145, (1959)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Y. Aharonov, D. Bohm, Phys. Rev. 123 (4) 1511, (1961)CrossRefMathSciNetADSGoogle Scholar
  16. 16.
    P. A. Horvathy, Classical Action, the Wu-Yang Phase Factor and Prequantiza-tion, in Proc. conf. , Aix-en-Provance, Salamanca. Lecture notes in mathematics, vol. 836 (Springer, Berlin Heidelberg New York, 1980), pp. 67-90. 1980Google Scholar
  17. 17.
    T. T. Wu, C. N. Yang, Phys. Rev. D12, 3845, (1975)MathSciNetADSGoogle Scholar
  18. 18.
    I. A. Dynnikov, Semiclassical motion of the electron. A proof of the Novikov con-jecture in general position and counterexamples, Solitons, Geometry and Topol-ogy: on the Crossroad (V. M. Buchstaber, ed. ), Am. Math. Soc. Transl. 179(2), 45-73 (1997)MathSciNetGoogle Scholar
  19. 19.
    I. A. Dynnikov, Russ. Math. Surveys 54 (1) 21-60, (1999)zbMATHCrossRefMathSciNetADSGoogle Scholar
  20. 20.
    G. D. Mostow, Ann. Math. 73, 20-48, (1961)CrossRefMathSciNetGoogle Scholar
  21. 21.
    L. Ausllander, L. Green, F. Hahn, Ann. Math. Stud. 53, (Princeton University Press Princeton, NJ, 1963) p. 107Google Scholar
  22. 22.
    J. W. Milnor, Morse theory, (Princeton University Press, Princeton, NJ 1963)zbMATHGoogle Scholar
  23. 23.
    S. Raghunathan, Discrete subgroups of Lie groups, (Springer, Berlin Heidelberg New York) 1972zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • D. V. Millionschikov
    • 1
  1. 1.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

Personalised recommendations