Isolated singularities of hypersurfaces
Geometric Topology
2023-06-13 v3
Abstract
Introduced by Seifert and Threlfall, cylindrical neighborhoods is an essential tool in the Lusternik-Schnirelmann theory. We conjecture that every isolated critical point of a smooth function admits a cylindrical ball neighborhood. We show that the conjecture is true for cone-like critical points, Cornea reasonable critical points, and critical points that satisfy the Rothe H hypothesis. In particular, the conjecture holds true at least for those critical points that are not infinitely degenerate.
Cite
@article{arxiv.2207.10072,
title = {Isolated singularities of hypersurfaces},
author = {Rustam Sadykov and Stanislav Trunov},
journal= {arXiv preprint arXiv:2207.10072},
year = {2023}
}
Comments
15 pages