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


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.


Compact Manifold Smooth Submanifolds Critical Circle Poincar6 Duality Connected Level 
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    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
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    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

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  • O. P. Bondar’

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