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

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. When Atiyah introduced L-Betti numbers for compact manifolds (later generalized to finite CW-complexes), he asked [1, p. 72] about the possible values these can assume. In particular, he asked whether they are always rational numbers, or even integers if the fundamental group is torsion free. This question was later popularized in precise form as “the strong Atiyah conjecture”. Easy ∗e-mail: [email protected] www: http://www.math.vt.edu/people/plinnell/ partially supported by a grant from the NSA. †e-mail: [email protected] www: http://www.uwm.edu/̃ okun ‡e-mail: [email protected] www: http://www.uni-math.gwdg.de/schick partially funded by the Courant Research Center “Higher order structures in Mathematics” within the German initiative of excellence