The homology of the Higman–Thompson groups
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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.
Originalsprog | Engelsk |
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Tidsskrift | Inventiones Mathematicae |
Vol/bind | 216 |
Udgave nummer | 2 |
Sider (fra-til) | 445–518 |
ISSN | 0020-9910 |
DOI | |
Status | Udgivet - 2019 |
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