Combinatorial modifications of Reeb graphs and the realization problem
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2018
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910351328542720 |
|---|---|
| author | Michalak, Łukasz Patryk |
| author_facet | Michalak, Łukasz Patryk |
| contents | We prove that, up to homeomorphism, any graph subject to natural necessary conditions on orientation and the cycle rank can be realized as the Reeb graph of a Morse function on a given closed manifold $M$. Along the way, we show that the Reeb number $\mathcal{R}(M)$, i.e. the maximum cycle rank among all Reeb graphs of functions on $M$, is equal to the corank of fundamental group $π_1(M)$, thus extending a previous result of Gelbukh to the non-orientable case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_08031 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Combinatorial modifications of Reeb graphs and the realization problem Michalak, Łukasz Patryk Geometric Topology 05C76, 57M15, 05C38 We prove that, up to homeomorphism, any graph subject to natural necessary conditions on orientation and the cycle rank can be realized as the Reeb graph of a Morse function on a given closed manifold $M$. Along the way, we show that the Reeb number $\mathcal{R}(M)$, i.e. the maximum cycle rank among all Reeb graphs of functions on $M$, is equal to the corank of fundamental group $π_1(M)$, thus extending a previous result of Gelbukh to the non-orientable case. |
| title | Combinatorial modifications of Reeb graphs and the realization problem |
| topic | Geometric Topology 05C76, 57M15, 05C38 |
| url | https://arxiv.org/abs/1811.08031 |