Blown-up corona of relatively hyperbolic groups
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917591970217984 |
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| author | Fukaya, Tomohiro |
| author_facet | Fukaya, Tomohiro |
| contents | We show that under appropriate assumptions, a blown-up corona of a relatively hyperbolic group is equivariant and the compactification of the universal space for proper action by the blown-up corona is contractible. As a corollary, we establish the formula to determine the covering dimension of the blown-up corona by the cohomological dimension of the group. We also show that the blown-up corona of a hyperbolic group with respect to an almost malnormal family of quasiconvex subgroups is homeomorphic to the Gromov boundary of the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blown-up corona of relatively hyperbolic groups Fukaya, Tomohiro Group Theory Geometric Topology 20F65 We show that under appropriate assumptions, a blown-up corona of a relatively hyperbolic group is equivariant and the compactification of the universal space for proper action by the blown-up corona is contractible. As a corollary, we establish the formula to determine the covering dimension of the blown-up corona by the cohomological dimension of the group. We also show that the blown-up corona of a hyperbolic group with respect to an almost malnormal family of quasiconvex subgroups is homeomorphic to the Gromov boundary of the group. |
| title | Blown-up corona of relatively hyperbolic groups |
| topic | Group Theory Geometric Topology 20F65 |
| url | https://arxiv.org/abs/2402.11501 |