Generalized Morse theory for tubular neighborhoods
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915408629465088 |
|---|---|
| author | Commaret, Antoine |
| author_facet | Commaret, Antoine |
| contents | We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Using non-smooth analysis and tools from geometric measure theory, we prove that the homotopy type of the sublevels sets of these Morse functions changes at a critical value by gluing exactly one cell around each critical point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04034 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Morse theory for tubular neighborhoods Commaret, Antoine Geometric Topology Metric Geometry 57R10 (Primary) 57N99, 26B12, 49Q15 (Secondary) We define a notion of Morse function and establish Morse theory-like theorems over offsets of any compact set in a Euclidean space at regular values of their distance function. Using non-smooth analysis and tools from geometric measure theory, we prove that the homotopy type of the sublevels sets of these Morse functions changes at a critical value by gluing exactly one cell around each critical point. |
| title | Generalized Morse theory for tubular neighborhoods |
| topic | Geometric Topology Metric Geometry 57R10 (Primary) 57N99, 26B12, 49Q15 (Secondary) |
| url | https://arxiv.org/abs/2401.04034 |