Approximating L^2-invariants and homology growth

Details Approximating L^2-invariants and homology growth Approximating L^2-invariants and homology growth

2012-03-13

arxiv.org/abs/1203.2827v2

Mathematics

Algebraic Topology

34 pages, in version v1 the list of references was mssing

Scientific paper

In this paper we consider the asymptotic behavior of invariants such as Betti numbers, minimal numbers of generators of singular homology, the order of the torsion subgroup of singular homology, and torsion invariants. We will show that all these vanish in the limit if the CW-complex under consideration fibers in a specific way. In particular we will show that all these vanish in the limit if one considers an aspherical closed manifold which admits a non-trivial S^1-action or whose fundamental group contains an infinite normal elementary amenable subgroup. By considering classifying spaces we also get results for groups.

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