2022/11/28 by Petrosyan, Nansen, Vankov, Vladimir
#20F65 #20F67 (Primary) 57M07 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2211.15575
We generalise a theorem of Gersten on surjectivity of the restriction map in ℓ∞-cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and ℓ∞-cohomology calculations for some well-known classes of groups. Along the way, we obtain hyperbolicity criteria for groups of type FP2(\mathbb Q) and for those satisfying a rational homological linear isoperimetric inequality, answering a question of Arora and Martínez-Pedroza.