Nikolay Nikolov: On growth of homology torsion in amenable groups

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology and the Workshop: New directions in L2-invariants (05.10.2016)

Suppose an amenable group G is acting freely on a simply connected simplicial complex X~ with compact quotient X. Fix n ≥ 1, assume Hn(X~, 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~/Hi 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.

Joint work with Aditi Kar and Peter Kropholler.