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.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
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