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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 ^ -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 et al. (Wed,) studied this question.
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