A Subgroup Theorem for Homological Filling Functions

2014/06/04 by Richard Gaelan Hanlon, Hanlon, Richard Gaelan, Eduardo Martinez-Pedroza +1
Mathematics · #20F65 #20F67 #20F69 #20J05 #57M07 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F65 #msc:20F67 #msc:20F69 #msc:20J05 #msc:57M07

paper · pdf · doi:10.48550/arxiv.1406.1046

Version accepted for publication in Groups, Geometry and Dynamics

arxiv created 2015/08/20 · arxiv updated 2015/08/21

Abstract

We use algebraic techniques to study homological filling functions of groups and their subgroups. If G is a group admitting a finite (n+1)--dimensional K(G,1) and H ≤ G is of type F_n+1, then the n^th--homological filling function of H is bounded above by that of G. This contrast with known examples where such inequality does not hold under weaker conditions on the ambient group G or the subgroup H. We include applications to hyperbolic groups and homotopical filling functions.

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