Vol. 11, No. 4, 2018

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Finiteness of homological filling functions

Joshua W. Fleming and Eduardo Martínez-Pedroza

Vol. 11 (2018), No. 4, 569–583

Let G be a group. For any G-module M and any integer d > 0, we define a function FVMd+1 : {} generalizing the notion of (d+1)-dimensional filling function of a group. We prove that this function takes only finite values if M is of type FPd+1 and d > 0, and remark that the asymptotic growth class of this function is an invariant of M. In the particular case that G is a group of type FPd+1, our main result implies that its (d+1)-dimensional homological filling function takes only finite values.

Dehn functions, homological filling function, isoperimetric inequalities, finiteness properties of groups
Mathematical Subject Classification 2010
Primary: 20F65, 20J05
Secondary: 16P99, 28A75, 57M07
Received: 15 September 2016
Accepted: 22 July 2017
Published: 15 January 2018

Communicated by Kenneth S. Berenhaut
Joshua W. Fleming
Memorial University of Newfoundland
St. John’s, NL
Eduardo Martínez-Pedroza
Memorial University of Newfoundland
St. John’s, NL