Mathematical Proceedings of the Cambridge Philosophical Society
Volume 162 Issue 2
On growth of homology torsion in amenable groups
Published online by Cambridge University Press: 14 July 2016
ADITI KAR ,
PETER KROPHOLLER and
NIKOLAY NIKOLOV
ADITI KAR
University of Southampton e-mails: a.kar@soton.ac.uk; p.h.kropholler@soton.ac.uk
PETER KROPHOLLER
University of Oxford e-mail: nikolov@maths.ox.ac.uk
a.kar@soton.ac.uk ;
p.h.kropholler@soton.ac.uk ;
nikolov@maths.ox.ac.uk
Suppose an amenable group G is acting freely on a simply connected simplicial complex $\~{X}$ with compact quotient X. Fix n ≥ 1, assume $H_n(\~{X}, \mathbb{Z}) = 0$ and let (Hi ) be a Farber chain in G. We prove that the torsion of the integral homology in dimension n of $\~{X}/H_i$ 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.
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 2 , March 2017 , pp. 337 - 351
Copyright © Cambridge Philosophical Society 2016
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ADITI KAR (a1), PETER KROPHOLLER (a1) and NIKOLAY NIKOLOV (a2)