The Strong Atiyah conjecture for virtually cocompact special groups

TL;DR

This paper establishes new conditions under which the Strong Atiyah conjecture can be extended to finite group extensions, demonstrating its validity for virtually cocompact special groups.

Contribution

It introduces novel conditions for lifting the Strong Atiyah conjecture to finite extensions and proves these hold for cocompact special groups, confirming the conjecture in this class.

Findings

Strong Atiyah conjecture holds for virtually cocompact special groups

New conditions identified for lifting the conjecture to finite extensions

Cocompact special groups satisfy these conditions

Abstract

We provide new conditions for the Strong Atiyah conjecture to lift to finite group extensions. In particular, we show cocompact special groups satisfy these conditions, so the Strong Atiyah conjecture holds for virtually cocompact special groups.