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2018 Finiteness of homological filling functions
Joshua W. Fleming, Eduardo Martínez-Pedroza
Involve 11(4): 569-583 (2018). DOI: 10.2140/involve.2018.11.569

Abstract

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.

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Joshua W. Fleming. Eduardo Martínez-Pedroza. "Finiteness of homological filling functions." Involve 11 (4) 569 - 583, 2018. https://doi.org/10.2140/involve.2018.11.569

Information

Received: 15 September 2016; Accepted: 22 July 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864397
MathSciNet: MR3778913
Digital Object Identifier: 10.2140/involve.2018.11.569

Subjects:
Primary: 20F65 , 20J05
Secondary: 16P99 , 28A75 , 57M07

Keywords: Dehn functions , finiteness properties of groups , homological filling function , Isoperimetric inequalities

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 4 • 2018
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