Graphs of curves on infinite-type surfaces with mapping class group actions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2016
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916150577725440 |
|---|---|
| author | Durham, Matthew Gentry Fanoni, Federica Vlamis, Nicholas G. |
| author_facet | Durham, Matthew Gentry Fanoni, Federica Vlamis, Nicholas G. |
| contents | We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_00841 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Graphs of curves on infinite-type surfaces with mapping class group actions Durham, Matthew Gentry Fanoni, Federica Vlamis, Nicholas G. Geometric Topology Group Theory We study when the mapping class group of an infinite-type surface $S$ admits an action with unbounded orbits on a connected graph whose vertices are simple closed curves on $S$. We introduce a topological invariant for infinite-type surfaces that determines in many cases whether there is such an action. This allows us to conclude that, as non-locally compact topological groups, many big mapping class groups have nontrivial coarse geometry in the sense of Rosendal. |
| title | Graphs of curves on infinite-type surfaces with mapping class group actions |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/1611.00841 |