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S 1-Bott functions on manifolds

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We study S 1-Bott functions on compact smooth manifolds. In particular, we investigate S 1-invariant Bott functions on manifolds with circle action.

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References

  1. S. V. Matveev, A. T. Fomenko, and V. V. Sharko, “Round Morse functions and isoenergy surfaces of integrable Hamiltonian systems,” Mat. Sb., 135, No. 3, 325–345 (1988).

    Google Scholar 

  2. A. T. Fomenko and H. Zieschang, “On the topology of three-dimensional manifolds arising in Hamiltonian mechanics,” Dokl. Akad. Nauk SSSR, 294, No. 2, 283–287 (1987).

    MathSciNet  Google Scholar 

  3. D. Barden, “Simply connected five-manifolds,” Ann. Math., 82, No. 3, 365–385 (1965).

    Article  MathSciNet  MATH  Google Scholar 

  4. V. V. Sharko, Functions on Manifolds: Algebraic and Topological Aspects, American Mathematical Society, Providence, RI (1993).

    MATH  Google Scholar 

  5. D. Asimov, “Round handle and non-singular Morse–Smale flows,” Ann. Math., 102, No. 1, 41–54 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Bott, “Lectures on Morse theory, old and new,” Bull. Amer. Math. Soc., 7, No. 2, 331–358 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  7. J. Franks, “Morse–Smale flows and homotopy theory,” Topology, 18, No. 2, 199–215 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Franks, “Homology and dynamical systems,” CMBS Regional Conf. Ser. Math., Vol. 49, American Mathematical Society, Providence, RI (1982).

    Google Scholar 

  9. M. Kogan, “Existence of perfect Morse functions on spaces with semi-free circle action,” J. Symplectic Geom., 1, No. 3, 829–850 (2003).

    MathSciNet  MATH  Google Scholar 

  10. S. Smale, “On the structure of manifolds,” Amer. J. Math., 84, No. 3, 387–399 (1962).

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Miyoshi, “Foliated round surgery of codimension-one foliated manifolds,” Topology, 21, No. 3, 245–262 (1983).

    Article  MathSciNet  Google Scholar 

  12. J. W. Morgan, “Non-singular Morse–Smale flows on 3-dimensional manifolds,” Topology, 18, No. 1, 41–53 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. W. Morgan and T. G. Tian, Ricci Flow and the Poincaré Conjecture, American Mathematical Society, Providence, RI (2007).

    MATH  Google Scholar 

  14. V. V. Sharko, “New L 2-invariants of chain complexes and applications,” in: C*-Algebras and Elliptic Theory, Birkhäuser, Basel (2006), pp. 291–312.

    Chapter  Google Scholar 

  15. W. Thurston, “Existence of codimension-one foliation,” Ann. Math., 104, No. 2, 249–268 (1976).

    Article  MathSciNet  MATH  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 12, pp. 1685–1698, December, 2012.

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Repovš, D., Sharko, V. S 1-Bott functions on manifolds. Ukr Math J 64, 1903–1918 (2013). https://doi.org/10.1007/s11253-013-0759-9

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  • DOI: https://doi.org/10.1007/s11253-013-0759-9

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