We prove that Thompson's group V is acyclic, answering a 1992 question of
Brown in the positive. More generally, we identify the homology of the
Higman-Thompson groups Vn,r with the homology of the zeroth component of
the infinite loop space of the mod n−1 Moore spectrum. As V=V2,1, we
can deduce that this group is acyclic. Our proof involves establishing
homological stability with respect to r, as well as a computation of the
algebraic K-theory of the category of finitely generated free Cantor algebras
of any type n.Comment: 49 page