Hyperbolicity and bounded-valued cohomology

Abstract

AbstractWe generalise a theorem of Gersten on surjectivity of the restriction map in $$\ell ^{\infty }$$ ℓ ∞ -cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and $$\ell ^{\infty }$$ ℓ ∞ -cohomology calculations for some well-known classes of groups. Along the way, we obtain hyperbolicity criteria for groups of type $$FP_2({{\mathbb {Q}}})$$ F P 2 ( Q ) and for those satisfying a rational homological linear isoperimetric inequality, answering a question of Arora and Martínez-Pedroza.