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On growth of homology torsion in amenable groups

Abstract:

Suppose an amenable group $G$ is acting freely on a simply connected simplicial complex $\tilde X$ with compact quotient $X$. Fix $n \geq 1$, assume $H_n(\tilde X, \mathbb{Z})=0$ and let $(H_i)$ be a Farber chain in $G$. We prove that the torsion of the integral homology in dimension $n$ of $\tilde{X}/H_i$ grows subexponentially in $[G:H_i]$. 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. T...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/S030500411600058X

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More from this funder
Name:
Engineering and Physical Sciences Research Council
Funding agency for:
Kropholler, P
Grant:
N007128/1
Publisher:
Cambridge University Press
Journal:
Mathematical Proceedings of the Cambridge Philosophical Society More from this journal
Volume:
162
Issue:
2
Pages:
337-351
Publication date:
2016-07-14
Acceptance date:
2016-06-01
DOI:
EISSN:
1469-8064
ISSN:
0305-0041
Keywords:
Pubs id:
pubs:527431
UUID:
uuid:22b87993-de5f-4593-9dd7-7c21b8943360
Local pid:
pubs:527431
Source identifiers:
527431
Deposit date:
2016-06-15

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