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.
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References
O. P. Bondar’, “On the number of critical submanifolds of a function on a manifold,” Ukr. Mat. Zh., 45, No. 12, 1702–1705 (1993).
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).
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Bondar’, O.P. Generalized (CO)Homology length of a Manifold and functions with Singular Submanifolds. Ukr Math J 48, 947–951 (1996). https://doi.org/10.1007/BF02384179
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DOI: https://doi.org/10.1007/BF02384179