ℓ2-homology of the free group

We analyze the reduced ℓ2-homology groups of a finitely generated nonabelian free group, F. Specifically, the projection map onto the space of harmonic ℓ2-1-chains is explicitly described and a weak isomorphism from (ℓ2(F))rk(F)−1 to the space of harmonic ℓ2-1-chains is given.