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Ukrainian Mathematical Journal

, Volume 48, Issue 6, pp 947–951 | Cite as

Generalized (CO)Homology length of a Manifold and functions with Singular Submanifolds

  • O. P. Bondar’
Brief Communications
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Abstract

We introduce a topological invariant of a manifold. In terms of this invariant, we obtain an estimate for the generalized Lyustemik-Shnirel’man category of the manifold considered and an estimate for the minimal number of singular submanifolds of a function on this manifold.

Keywords

Compact Manifold Smooth Submanifolds Critical Circle Poincar6 Duality Connected Level 
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.

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References

  1. 1.
    O. P. Bondar’, “On the number of critical submanifolds of a function on a manifold,” Ukr. Mat. Zh., 45, No. 12, 1702–1705 (1993).MathSciNetGoogle Scholar
  2. 2.
    F. Takens, “The minimal number of critical points of a function on a compact manifold and the Lusternik-Shnirelman category,” Invent. Math., 6, 197–204 (1968).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • O. P. Bondar’

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