Amenable groups of finite cohomological dimension and the zero divisor conjecture

TL;DR

This paper proves that certain amenable groups with specific cohomological properties are solvable and explores homological finiteness related to the zero divisor conjecture and group actions on acyclic complexes.

Contribution

It establishes solvability for amenable groups of cohomological dimension two with domain group rings and investigates homological properties linked to the zero divisor conjecture.

Findings

Amenable groups of cohomological dimension two with domain group rings are solvable.

Connections between the zero divisor conjecture and homological finiteness properties.

Analysis of group actions on acyclic CW-complexes with amenable stabilisers.

Abstract

We prove that every amenable group of cohomological dimension two whose integral group ring is a domain is solvable and investigate certain homological finiteness properties of groups that satisfy the analytic zero divisor conjecture and act on an acyclic CW-complex with amenable stabilisers.