The strong Atiyah conjecture for right-angled Artin and Coxeter groups

TL;DR

This paper proves the strong Atiyah conjecture for right-angled Artin and Coxeter groups, including certain extensions, advancing understanding of their algebraic and topological properties.

Contribution

It establishes the strong Atiyah conjecture for a broad class of groups, including specific extensions of right-angled Artin and Coxeter groups.

Findings

Proved the conjecture for right-angled Artin groups.

Extended proof to certain finite and elementary amenable extensions.

Enhanced understanding of group properties related to the conjecture.

Abstract

We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.