The homology of the Higman–Thompson groups

TY - JOUR

T1 - The homology of the Higman–Thompson groups

AU - Szymik, Markus

AU - Wahl, Nathalie

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85064341310&partnerID=8YFLogxK

U2 - 10.1007/s00222-018-00848-z

DO - 10.1007/s00222-018-00848-z

M3 - Journal article

AN - SCOPUS:85064341310

SN - 0020-9910

VL - 216

SP - 445

EP - 518

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 2

ER -