A cubulation with no factor system
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916648612528128 |
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| author | Shepherd, Sam |
| author_facet | Shepherd, Sam |
| contents | The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10421 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A cubulation with no factor system Shepherd, Sam Group Theory 20F65 (Primary) 20F67 (Secondary) The primary method for showing that a given cubulated group is hierarchically hyperbolic is by constructing a factor system on the cube complex. In this paper we show that such a construction is not always possible, namely we construct a cubulated group for which the cube complex does not have a factor system. We also construct a cubulated group for which the induced action on the contact graph is not acylindrical. |
| title | A cubulation with no factor system |
| topic | Group Theory 20F65 (Primary) 20F67 (Secondary) |
| url | https://arxiv.org/abs/2208.10421 |