The homology of the Higman–Thompson groups

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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.

OriginalsprogEngelsk
TidsskriftInventiones Mathematicae
Vol/bind216
Udgave nummer2
Sider (fra-til)445–518
ISSN0020-9910
DOI
StatusUdgivet - 2019

ID: 223822211