# On growth of homology torsion in amenable groups

Kar, A
Nikolov, N
Kropholler, P

14 July 2016

## Journal:

Mathematical Proceedings of the Cambridge Philosophical Society

## Last Updated:

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

2

162

## DOI:

10.1017/S030500411600058X

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.

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