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Exact functions on manifolds

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Abstract

It is proved that the property of a manifold Mn possessing a smooth function with given numbers of critical points of each index is homotopic invariant if Wh(π 1 (Mn)) = 0 and every Z(π 1 (Mn))-stable free module is free.

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Literature cited

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

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    O. I. Bogoyavlenskii

Authors
  1. O. I. Bogoyavlenskii
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Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 77–83, July, 1970.

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Bogoyavlenskii, O.I. Exact functions on manifolds. Mathematical Notes of the Academy of Sciences of the USSR 8, 514–517 (1970). https://doi.org/10.1007/BF01093444

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  • DOI: https://doi.org/10.1007/BF01093444

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