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On growth of homology torsion in amenable groups

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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 , 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 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. These examples include some solvable groups of derived length 3 which is the minimal possible.

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