Abstract
We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X1 ,...,X n of generators of the group algebra CG, Voiculescu's non-microstates free entropy dimension δ ∗ (X1 ,...,X n) is exactly equal to β1(G) − β0(G )+1 , whereβi are the � 2 -Betti numbers of G.
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