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Cohomological Characterisation of Hyperbolicity
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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.
Oxford University Press (OUP)
Title: Cohomological Characterisation of Hyperbolicity
Description:
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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