Non-singular extensions of circle-valued Morse functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908935115505664 |
|---|---|
| author | Iwakura, Koki |
| author_facet | Iwakura, Koki |
| contents | In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular extension of a circle-valued Morse function as the main theorem when a submersion on a collar neighborhood is given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07309 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-singular extensions of circle-valued Morse functions Iwakura, Koki Geometric Topology 58K05, 58K15, 58K30 In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular extension of a circle-valued Morse function as the main theorem when a submersion on a collar neighborhood is given. |
| title | Non-singular extensions of circle-valued Morse functions |
| topic | Geometric Topology 58K05, 58K15, 58K30 |
| url | https://arxiv.org/abs/2311.07309 |