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Morse theory of closed 1-forms

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Algebraic Topology Poznań 1989

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1474))

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References

  1. Novikov S. P. Multivalued functions and functionals analogue of Morse theory. Dokl. AN SSSR, 1981, v.270, N 1, p. 31–35 (in Russ.).

    MathSciNet  MATH  Google Scholar 

  2. Novikov S. P. Hamiltonian formalism and multivalued analogue of Morse theory. Russ. Math. Surveys, 1982, v.37, N 5, p. 3–49 (in Russ.).

    Article  MathSciNet  Google Scholar 

  3. Novikov S. P., Smeltzer I. Periodic solutions of the Kirchhof type equations for the free motion of the solid body in the liquid and the extended Lusternik-Schnirelman-Morse theory (L-Sch-M) I. Funkz. anal. i pril. 1981, v.15, N 3, p. 54–66 (in Russ.).

    Google Scholar 

  4. Smale S. On the structure of mainfolds. Amer. J. Math. 1962, v.84, p. 387–399.

    Article  MathSciNet  MATH  Google Scholar 

  5. Farber M. Sh. The exactness of Novikov inequalities. Funcz. anal. i pril. 1985, v.19, N 1, p. 49–59 (in Russ.).

    MathSciNet  MATH  Google Scholar 

  6. Novikov S. P. Bloch homology. Critical points of functions and closed 1-forms. Dokl. AN SSSR, 1987, v.287, N 6, p. 1321–1324.

    MathSciNet  Google Scholar 

  7. Pazhitnov A. V. An analytic proof of the real part of Novikov's inequalities. Dokl. AN SSSR 1987, v.293, N 6, p. 1305–1307.

    MathSciNet  MATH  Google Scholar 

  8. Pazhitnov A. V. Proof of Novikov's coniecture on homology with local coefficients over a field of finite characteristic. Dokl. AN SSSR. 1988, v.300, N 6, p. 1316–1320.

    MathSciNet  MATH  Google Scholar 

  9. Pazhitnov A. V. On the exactness of Novikov type inequalities for π1 M = Zm and Morse forms within the generic cohomology classes. Dokl. AN SSSR. 1989, v.306, N 4, p. 544–548.

    MathSciNet  Google Scholar 

  10. Pazhitnov A. V. On the exactness of Novikov inequalities for the manifolds with free abelian fundamental group. Mat. Sbornik 1989, v.180, N 11, p. 1486–1523.

    MathSciNet  MATH  Google Scholar 

  11. Witten E. Supersymmetry and Morse theory. Journal of differential geometry, 1982, v.17, p. 661–692.

    MathSciNet  MATH  Google Scholar 

  12. Milnor J. W. Infinite cyclic coverings. In: Conference on the topology of Manifolds (edited by J.G. Hocking) Prindle Weber & Schmidt 1968, p. 115–133.

    Google Scholar 

  13. Kraines D. Higher order Massey products. Transactions of American mathematical society 1966, v.124, N 5, p. 431–439.

    Article  MathSciNet  MATH  Google Scholar 

  14. Bousfield A. K., Gugenheim V. K. A. M. On PL deRham theory and rational homotopy type. Memoirs of the American Mathematical Society, 1976, v.8, number 179.

    Google Scholar 

  15. Milnor J. W. Lectures on the h-cobordism theorem. Princeton 1965.

    Google Scholar 

  16. Sharko V. V. K-theory and Morse theory 1. Preprint Kiev Inst. of Math. AN SSSR 1986, N 86.39.

    Google Scholar 

  17. Browder W., Levine J. Fibering manifolds over a circle. Comment. Math. Helv. v.40, 1966, p. 153–160.

    Article  MathSciNet  MATH  Google Scholar 

  18. Farrell F. T. The obstruction to fibering a manifold over a circle. Indiana Univ. Math. Journ. 1971, v.21, N 4, p. 315–346.

    Article  MathSciNet  MATH  Google Scholar 

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Stefan Jackowski Bob Oliver Krzystof Pawałowski

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© 1991 Springer-Verlag

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Pazhitnov, A.V. (1991). Morse theory of closed 1-forms. In: Jackowski, S., Oliver, B., Pawałowski, K. (eds) Algebraic Topology Poznań 1989. Lecture Notes in Mathematics, vol 1474. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084740

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  • DOI: https://doi.org/10.1007/BFb0084740

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  • Print ISBN: 978-3-540-54098-4

  • Online ISBN: 978-3-540-47403-6

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