Cohomological characterisation of hyperbolicity
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912730072481792 |
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| author | Milizia, Francesco Petrosyan, Nansen Sisto, Alessandro Vankov, Vladimir |
| author_facet | Milizia, Francesco Petrosyan, Nansen Sisto, Alessandro Vankov, Vladimir |
| contents | For any geodesic metric space $X$, we give a complete cohomological characterisation of the hyperbolicity of $X$ in terms of vanishing of its second $\ell^{\infty}$-cohomology. We extend this result to the relative setting of $X$ with a collection of uniformly hyperbolic subgraphs. As an application, we give a cohomological characterisation of acylindrical hyperbolicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomological characterisation of hyperbolicity Milizia, Francesco Petrosyan, Nansen Sisto, Alessandro Vankov, Vladimir Group Theory Algebraic Topology Functional Analysis Geometric Topology 20F65 (Primary) 20F67, 57M07 (Secondary) For any geodesic metric space $X$, we give a complete cohomological characterisation of the hyperbolicity of $X$ in terms of vanishing of its second $\ell^{\infty}$-cohomology. We extend this result to the relative setting of $X$ with a collection of uniformly hyperbolic subgraphs. As an application, we give a cohomological characterisation of acylindrical hyperbolicity. |
| title | Cohomological characterisation of hyperbolicity |
| topic | Group Theory Algebraic Topology Functional Analysis Geometric Topology 20F65 (Primary) 20F67, 57M07 (Secondary) |
| url | https://arxiv.org/abs/2409.18871 |