Orderability of big mapping class groups
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916352097255424 |
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| author | Kumar, Pravin Sanghi, Apeksha Singh, Mahender |
| author_facet | Kumar, Pravin Sanghi, Apeksha Singh, Mahender |
| contents | We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander system for the surface using a carefully chosen exhaustion by finite-type subsurfaces. In fact, we prove that a generalised ideal arc system for the surface also induces a left-ordering on the big mapping class group. We then prove that two generalised ideal arc systems determine the same left-ordering if and only if they are loosely isotopic. Finally, we prove that the topology on the big mapping class group is the same as the order topology induced by a left-ordering corresponding to an inductively constructed ideal arc system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orderability of big mapping class groups Kumar, Pravin Sanghi, Apeksha Singh, Mahender Geometric Topology Group Theory Primary 06F15, 20F60, Secondary 57K20 We give an alternate proof of the left-orderability of the mapping class group of a connected oriented infinite-type surface with a non-empty boundary. Our main strategy involves the inductive construction of a countable stable Alexander system for the surface using a carefully chosen exhaustion by finite-type subsurfaces. In fact, we prove that a generalised ideal arc system for the surface also induces a left-ordering on the big mapping class group. We then prove that two generalised ideal arc systems determine the same left-ordering if and only if they are loosely isotopic. Finally, we prove that the topology on the big mapping class group is the same as the order topology induced by a left-ordering corresponding to an inductively constructed ideal arc system. |
| title | Orderability of big mapping class groups |
| topic | Geometric Topology Group Theory Primary 06F15, 20F60, Secondary 57K20 |
| url | https://arxiv.org/abs/2407.14343 |