On the Čech cohomology of Morse boundaries
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908907398496256 |
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| author | Fioravanti, Elia Karrer, Annette Sisto, Alessandro Zbinden, Stefanie |
| author_facet | Fioravanti, Elia Karrer, Annette Sisto, Alessandro Zbinden, Stefanie |
| contents | We consider cusped hyperbolic $n-$manifolds, and compute Čech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced Čech cohomology with real coefficients vanishes in dimension at most $n-3$ and does not vanish in dimension $n-2$. A similar result holds for relatively hyperbolic groups with virtually nilpotent peripherals and Bowditch boundary homeomorphic to a sphere; these include all non-uniform lattices in rank$-1$ simple Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Čech cohomology of Morse boundaries Fioravanti, Elia Karrer, Annette Sisto, Alessandro Zbinden, Stefanie Group Theory Geometric Topology We consider cusped hyperbolic $n-$manifolds, and compute Čech cohomology groups of the Morse boundaries of their fundamental groups. In particular, we show that the reduced Čech cohomology with real coefficients vanishes in dimension at most $n-3$ and does not vanish in dimension $n-2$. A similar result holds for relatively hyperbolic groups with virtually nilpotent peripherals and Bowditch boundary homeomorphic to a sphere; these include all non-uniform lattices in rank$-1$ simple Lie groups. |
| title | On the Čech cohomology of Morse boundaries |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2303.15981 |