The homology of the Higman-Thompson groups
成果类型：
Article
署名作者：
Szymik, Markus; Wahl, Nathalie
署名单位：
Norwegian University of Science & Technology (NTNU); University of Copenhagen
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-018-00848-z
发表日期：
2019
页码：
445-518
关键词：
摘要：
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,V-r with the homology of the zeroth component of the infinite loop space of the mod n - 1 Moore spectrum. As V = V-2,V-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.
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