On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups
Group Theory
2026-04-21 v2
Abstract
We investigate the action of the automorphism group of an acylindrically hyperbolic group G on its space of homogeneous quasimorphisms, and identify its kernel with the subgroup of "strongly commensurating" automorphisms. We deduce that if G has no non-trivial finite normal subgroups then it has sufficiently many quasimorphisms to recognize whether an automorphism is inner. As consequences, we show that Out(G) acts faithfully on the kernel of the comparison map in bounded cohomology and it embeds in (several) groups of coarse automorphisms.
Keywords
Cite
@article{arxiv.2509.04238,
title = {On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups},
author = {Ashot Minasyan and Alessandro Sisto and Federico Vigolo},
journal= {arXiv preprint arXiv:2509.04238},
year = {2026}
}
Comments
Minor changes, accepted for publication in Comm. Math. Helv., 16 pages