The homology of the Higman–Thompson groups
Tóm tắt
We prove that Thompson’s group
$$\mathrm {V}$$
is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman–Thompson groups
$$\mathrm {V}_{n,r}$$
with the homology of the zeroth component of the infinite loop space of the mod
$$n-1$$
Moore spectrum. As
$$\mathrm {V}=\mathrm {V}_{2,1}$$
, 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.
Từ khóa
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