On growth of homology torsion in amenable groups
2016 ◽
Vol 162
(2)
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pp. 337-351
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Keyword(s):
AbstractSuppose 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.
2020 ◽
Vol 2020
(766)
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pp. 45-60
1992 ◽
Vol 52
(2)
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pp. 237-241
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2005 ◽
Vol 15
(04)
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pp. 619-642
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1995 ◽
Vol 58
(2)
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pp. 219-221
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1991 ◽
Vol 34
(3)
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pp. 423-425
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2001 ◽
Vol 44
(2)
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pp. 231-241
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2008 ◽
Vol 28
(1)
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pp. 87-124
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2016 ◽
Vol 09
(02)
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pp. 1650037
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1988 ◽
Vol 30
(3)
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pp. 331-337
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