The homology of the Higman–Thompson groups

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The homology of the Higman–Thompson groups. / Szymik, Markus; Wahl, Nathalie.

In: Inventiones Mathematicae, Vol. 216, No. 2, 2019, p. 445–518.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Szymik, M & Wahl, N 2019, 'The homology of the Higman–Thompson groups', Inventiones Mathematicae, vol. 216, no. 2, pp. 445–518. https://doi.org/10.1007/s00222-018-00848-z

APA

Szymik, M., & Wahl, N. (2019). The homology of the Higman–Thompson groups. Inventiones Mathematicae, 216(2), 445–518. https://doi.org/10.1007/s00222-018-00848-z

Vancouver

Szymik M, Wahl N. The homology of the Higman–Thompson groups. Inventiones Mathematicae. 2019;216(2):445–518. https://doi.org/10.1007/s00222-018-00848-z

Author

Szymik, Markus ; Wahl, Nathalie. / The homology of the Higman–Thompson groups. In: Inventiones Mathematicae. 2019 ; Vol. 216, No. 2. pp. 445–518.

Bibtex

@article{9c1a61d60ef7494c85b0910e33df5c02,
title = "The homology of the Higman–Thompson groups",
abstract = " We prove that Thompson{\textquoteright}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. ",
author = "Markus Szymik and Nathalie Wahl",
year = "2019",
doi = "10.1007/s00222-018-00848-z",
language = "English",
volume = "216",
pages = "445–518",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer",
number = "2",

}

RIS

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