On growth of homology torsion in amenable groups

Author: 

Kar, A
Nikolov, N
Kropholler, P

Publication Date: 

14 July 2016

Journal: 

Mathematical Proceedings of the Cambridge Philosophical Society

Last Updated: 

2020-01-22T07:30:22.403+00:00

Issue: 

2

Volume: 

162

DOI: 

10.1017/S030500411600058X

page: 

337-351

abstract: 

Suppose an amenable group G is acting freely on a simply connected simplicial complex (Formula presented.) with compact quotient X. Fix n ≥ 1, assume (Formula presented.) and let (Hi ) be a Farber chain in G. We prove that the torsion of the integral homology in dimension n of (Formula presented.) grows subexponentially in [G : Hi ]. This fails if X is not compact. We provide the first examples of amenable groups for which torsion in homology grows faster than any given function. These examples include some solvable groups of derived length 3 which is the minimal possible.

Symplectic id: 

527431

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article