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.
Milizia, F., Petrosyan, N., Sisto, A., Vankov, V. (2025). Cohomological Characterisation of Hyperbolicity. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2025(24), 1-23 [10.1093/imrn/rnaf353].
Cohomological Characterisation of Hyperbolicity
Milizia, Francesco;
2025
Abstract
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.File in questo prodotto:
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Hyperbolically_Embedded_Subgroup.pdf
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