Bondar' O. P.
Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1431–1432
In terms of the Euler characteristic, we obtain the condition of existence of Bott functions on differentiable manifolds that have a set of critical points formed by connected homeomorphic submanifolds.
Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 843-846
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.
Ukr. Mat. Zh. - 1993. - 45, № 12. - pp. 1702–1705
We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of these functions.