Non-microstates free entropy dimension for groups
arXiv:math/0312242
Abstract
We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X_1,...,X_n of generators of the group algebra of G, Voiculescu's non-microstates free entropy dimension δ^*(X_1,...,X_n) is exactly equal to β_1 (G)-β_0 (G)+1, where β_i are the L^2 Betti numbers of G.
Revised version. Some explanations added and several typos fixed. To appear in Geom. and Func. Anal