Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917819303591936 |
|---|---|
| author | Dickmann, Ryan Hoganson, Hannah Kwak, Sanghoon |
| author_facet | Dickmann, Ryan Hoganson, Hannah Kwak, Sanghoon |
| contents | Motivated by the recent work of Algom-Kfir and Bestinva introducing the mapping class group of an infinite graph via proper homotopy equivalences, we give a necessary and sufficient condition for a surface to be properly homotopy equivalent to a graph. We consider second-countable orientable surfaces that are possibly infinite-type and have noncompact boundary. For surfaces proper homotopy equivalent to graphs, we explore the basic properties of the induced map between the mapping class groups of the surface and the graph. We view this induced map as the basis of a Dehn-Nielsen-Baer analog in the setting of infinite-type surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps Dickmann, Ryan Hoganson, Hannah Kwak, Sanghoon Geometric Topology Group Theory Motivated by the recent work of Algom-Kfir and Bestinva introducing the mapping class group of an infinite graph via proper homotopy equivalences, we give a necessary and sufficient condition for a surface to be properly homotopy equivalent to a graph. We consider second-countable orientable surfaces that are possibly infinite-type and have noncompact boundary. For surfaces proper homotopy equivalent to graphs, we explore the basic properties of the induced map between the mapping class groups of the surface and the graph. We view this induced map as the basis of a Dehn-Nielsen-Baer analog in the setting of infinite-type surfaces. |
| title | Surfaces proper homotopy equivalent to graphs and their Dehn-Nielsen-Baer maps |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2410.20877 |