The homology of the Higman–Thompson groups
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The homology of the Higman–Thompson groups. / Szymik, Markus; Wahl, Nathalie.
I: Inventiones Mathematicae, Bind 216, Nr. 2, 2019, s. 445–518.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - The homology of the Higman–Thompson groups
AU - Szymik, Markus
AU - Wahl, Nathalie
PY - 2019
Y1 - 2019
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
VL - 216
SP - 445
EP - 518
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 2
ER -
ID: 223822211