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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.00124 |
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| _version_ | 1866909767167901696 |
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| author | Hill, Thomas |
| author_facet | Hill, Thomas |
| contents | The work of Mann and Rafi gives a classification surfaces $Σ$ when $\textrm{Map}(Σ)$ is globally CB, locally CB, and CB generated under the technical assumption of tameness. In this article, we restrict our study to the pure mapping class group and give a complete classification without additional assumptions. In stark contrast with the rich class of examples of Mann--Rafi, we prove that $\textrm{PMap}(Σ)$ is globally CB if and only if $Σ$ is the Loch Ness monster surface, and locally CB or CB generated if and only if $Σ$ has finitely many ends and is not a Loch Ness monster surface with (nonzero) punctures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00124 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large-Scale Geometry of Pure Mapping Class Groups of Infinite-Type Surfaces Hill, Thomas Geometric Topology Group Theory 57K20 The work of Mann and Rafi gives a classification surfaces $Σ$ when $\textrm{Map}(Σ)$ is globally CB, locally CB, and CB generated under the technical assumption of tameness. In this article, we restrict our study to the pure mapping class group and give a complete classification without additional assumptions. In stark contrast with the rich class of examples of Mann--Rafi, we prove that $\textrm{PMap}(Σ)$ is globally CB if and only if $Σ$ is the Loch Ness monster surface, and locally CB or CB generated if and only if $Σ$ has finitely many ends and is not a Loch Ness monster surface with (nonzero) punctures. |
| title | Large-Scale Geometry of Pure Mapping Class Groups of Infinite-Type Surfaces |
| topic | Geometric Topology Group Theory 57K20 |
| url | https://arxiv.org/abs/2309.00124 |