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arXiv · 2409.18871

Cohomological characterisation of hyperbolicity

Francesco Milizia·Nansen Petrosyan·Alessandro Sisto·Vladimir Vankov
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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.

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Francesco Milizia, Nansen Petrosyan, Alessandro Sisto, Vladimir Vankov. 2024-09-27. Cohomological characterisation of hyperbolicity. https://arxiv.org/abs/2409.18871

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