Atiyah’s L 2-index theorem, Kan-Thurston construction, and weak Bass conjecture

Abstract

We conjecture that for a group G of type FP, the L2-Euler characteristic of a group G is the same as the ordinary Euler characteristic of G, and show that this conjecture is closely related with the weak Bass conjecture. We also present a class of groups satisfying this conjecture. Ourmethod combines the Kan-Thurston construction, Atiyah’s L2-index theorem, and a result of Berrick, Chatterji, and Mislin.