English

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.

Keywords

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

R2 v1 2026-06-25T01:05:31.801Z