Finite index rigidity of hyperbolic groups
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910646730227712 |
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| author | Lazarovich, Nir |
| author_facet | Lazarovich, Nir |
| contents | We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a graph to the minimal number of cells in a simplicial classifying space for the group. As a corollary we prove that any two isomorphic finite-index subgroups of a non-elementary hyperbolic group have the same index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04484 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Finite index rigidity of hyperbolic groups Lazarovich, Nir Group Theory Metric Geometry 20F67, 20F65 We prove that the topological complexity of a finite index subgroup of a hyperbolic group is linear in its index. This follows from a more general result relating the size of the quotient of a free cocompact action of hyperbolic group on a graph to the minimal number of cells in a simplicial classifying space for the group. As a corollary we prove that any two isomorphic finite-index subgroups of a non-elementary hyperbolic group have the same index. |
| title | Finite index rigidity of hyperbolic groups |
| topic | Group Theory Metric Geometry 20F67, 20F65 |
| url | https://arxiv.org/abs/2302.04484 |