Year: 2025
Type: article
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.
DOI: 10.1093/imrn/rnaf353
Authors: Francesco Milizia, Nansen Petrosyan, Alessandro Sisto, Vladimir Vankov
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417287384