From the second BNSR invariant to Dehn functions of coabelian subgroups

2024/04/18 by Isenrich, Claudio Llosa · 1 citation
#20F05 #20F06 #20F65 #20F67 #20F69 #20J05 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2404.12334

Abstract

Given a finitely presented group G and a surjective homomorphism G→ ℤⁿ with finitely presented kernel K, we give an upper bound on the Dehn function of K in terms of an area-radius pair for G. As a consequence we obtain that finitely presented coabelian subgroups of hyperbolic groups have polynomially bounded Dehn function. This generalises results of Gersten and Short and our proof can be viewed as a quantified version of results from Renz' thesis on the second BNSR invariant.

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• Dense and empty BNSR-invariants of the McCool groups

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