CAT(0) and cubulated Shephard groups
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909432503336960 |
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| author | Goldman, Katherine |
| author_facet | Goldman, Katherine |
| contents | Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well known result that Coxeter groups are $\mathrm{CAT}(0)$ to a class of Shephard groups that have "enough" finite parabolic subgroups. We also show that in this setting, if the associated Coxeter group is type (FC), then the Shephard group acts properly and cocompactly on a $\mathrm{CAT}(0)$ cube complex. As part of our proof of the former result, we introduce a new criteria for a complex made of $A_3$ simplices to be $\mathrm{CAT}(1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | CAT(0) and cubulated Shephard groups Goldman, Katherine Group Theory Algebraic Topology Geometric Topology Metric Geometry 20F65 (Primary) 51F15, 57M60, 51M20 (Secondary) Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well known result that Coxeter groups are $\mathrm{CAT}(0)$ to a class of Shephard groups that have "enough" finite parabolic subgroups. We also show that in this setting, if the associated Coxeter group is type (FC), then the Shephard group acts properly and cocompactly on a $\mathrm{CAT}(0)$ cube complex. As part of our proof of the former result, we introduce a new criteria for a complex made of $A_3$ simplices to be $\mathrm{CAT}(1)$. |
| title | CAT(0) and cubulated Shephard groups |
| topic | Group Theory Algebraic Topology Geometric Topology Metric Geometry 20F65 (Primary) 51F15, 57M60, 51M20 (Secondary) |
| url | https://arxiv.org/abs/2310.10883 |