From the second BNSR invariant to Dehn functions of coabelian subgroups

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.