Cohomological characterisation of hyperbolicity

Francesco Milizia; Nansen Petrosyan; Alessandro Sisto; Vladimir Vankov

doi:10.1093/imrn/rnaf353

Cohomological characterisation of hyperbolicity

Francesco Milizia
, Nansen Petrosyan
, Alessandro Sisto
, Vladimir Vankov

Research output: Contribution to journal › Article › peer-review

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 ℓ^∞-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 a cylindrical hyperbolicity.

Original language	English
Article number	rnaf353
Journal	International Mathematics Research Notices
Volume	2025
Issue number	24
Early online date	12 Dec 2025
DOIs	https://doi.org/10.1093/imrn/rnaf353
Publication status	Published - Dec 2025

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This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record, Francesco Milizia, Nansen Petrosyan, Alessandro Sisto, Vladimir Vankov, Cohomological Characterisation of Hyperbolicity, International Mathematics Research Notices, Volume 2025, Issue 24, December 2025, rnaf353, is available online at https://doi.org/10.1093/imrn/rnaf353
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Cohomological characterisation of hyperbolicity

Abstract

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