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We show thatH3(l1(Z+);l1(Z+)0) = 0. We rst use the Connes- Tzygan exact sequence to prove that this is equivalent to the vanishing of the third cyclic cohomology groupHC3(I;I0), whereI is the non-unital Banach algebra l1(N), and then prove thatHC3(I;I0) = 0. 1. Preliminaries

Vanishing of the third simplicial cohomology group of $l^1(\mathbf {Z}_+)$