The homology of the Higman–Thompson groups

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Markus Szymik, Nathalie Wahl

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 V n , r with the homology of the zeroth component of the infinite loop space of the mod n- 1 Moore spectrum. As V = 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.

TidsskriftInventiones Mathematicae
Udgave nummer2
Sider (fra-til)445–518
StatusUdgivet - 2019

ID: 223822211