$P$-categories and functions with degenerate singular submanifolds

Olha Bondar

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arXiv · 2606.14809

$P$-categories and functions with degenerate singular submanifolds

Olha Bondar

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Abstract

We study smooth functions on manifolds whose sets of critical points is a disjoint union of submanifolds each diffeomorphic to the same manifold P. These submanifolds are not necessarily non-degenerate. We obtain sufficent conditions for existence of functions with minimal number of such submanifolds. This a translation from Ukrainian of PhD defended in 1993 at the Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine. Scientific advisor: Volodymyr Sharko.

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Olha Bondar. 2026-06-12. $P$-categories and functions with degenerate singular submanifolds. https://arxiv.org/abs/2606.14809

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