A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866913400193286144 |
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| author | Behrstock, Jason Hagen, Mark Martin, Alexandre Sisto, Alessandro |
| author_facet | Behrstock, Jason Hagen, Mark Martin, Alexandre Sisto, Alessandro |
| contents | We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic (and even relatively hyperbolic in the genus 2 case). Under residual finiteness assumptions, we construct many non-elementary hyperbolic quotients of mapping class groups. Using these quotients, we reduce questions of Reid and Bridson-Reid-Wilton about finite quotients of mapping class groups to residual finiteness of specific hyperbolic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_00567 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups Behrstock, Jason Hagen, Mark Martin, Alexandre Sisto, Alessandro Group Theory Geometric Topology We give a simple combinatorial criterion, in terms of an action on a hyperbolic simplicial complex, for a group to be hierarchically hyperbolic. We apply this to show that quotients of mapping class groups by large powers of Dehn twists are hierarchically hyperbolic (and even relatively hyperbolic in the genus 2 case). Under residual finiteness assumptions, we construct many non-elementary hyperbolic quotients of mapping class groups. Using these quotients, we reduce questions of Reid and Bridson-Reid-Wilton about finite quotients of mapping class groups to residual finiteness of specific hyperbolic groups. |
| title | A combinatorial take on hierarchical hyperbolicity and applications to quotients of mapping class groups |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2005.00567 |