Second mod 2 homology of artin groups

Toshiyuki Akita; Ye Liu

doi:10.2140/agt.2018.18.547

Second mod 2 homology of artin groups

Toshiyuki Akita, Ye Liu

Hokkaido University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π, 1) conjecture. The key ingredients are (A) Hopf’s formula for the second integral homology of a group and (B) Howlett’s result on the second integral homology of Coxeter groups.

Original language	English
Pages (from-to)	547-568
Number of pages	22
Journal	Algebraic and Geometric Topology
Volume	18
Issue number	1
DOIs	https://doi.org/10.2140/agt.2018.18.547
Publication status	Published - 10 Jan 2018
Externally published	Yes

Keywords

Artin groups
Coxeter groups
Group cohomology

Access to Document

10.2140/agt.2018.18.547

Cite this

Akita, T., & Liu, Y. (2018). Second mod 2 homology of artin groups. Algebraic and Geometric Topology, 18(1), 547-568. https://doi.org/10.2140/agt.2018.18.547

@article{827ffd63605a4f1db004e6453d0f44f4,

title = "Second mod 2 homology of artin groups",

abstract = "In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π, 1) conjecture. The key ingredients are (A) Hopf{\textquoteright}s formula for the second integral homology of a group and (B) Howlett{\textquoteright}s result on the second integral homology of Coxeter groups.",

keywords = "Artin groups, Coxeter groups, Group cohomology",

author = "Toshiyuki Akita and Ye Liu",

year = "2018",

month = jan,

day = "10",

doi = "10.2140/agt.2018.18.547",

language = "English",

volume = "18",

pages = "547--568",

journal = "Algebraic and Geometric Topology",

issn = "1472-2747",

number = "1",

}

TY - JOUR

T1 - Second mod 2 homology of artin groups

AU - Akita, Toshiyuki

AU - Liu, Ye

PY - 2018/1/10

Y1 - 2018/1/10

N2 - In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π, 1) conjecture. The key ingredients are (A) Hopf’s formula for the second integral homology of a group and (B) Howlett’s result on the second integral homology of Coxeter groups.

AB - In this paper, we compute the second mod 2 homology of an arbitrary Artin group, without assuming the K(π, 1) conjecture. The key ingredients are (A) Hopf’s formula for the second integral homology of a group and (B) Howlett’s result on the second integral homology of Coxeter groups.

KW - Artin groups

KW - Coxeter groups

KW - Group cohomology

UR - http://www.scopus.com/inward/record.url?scp=85040913629&partnerID=8YFLogxK

U2 - 10.2140/agt.2018.18.547

DO - 10.2140/agt.2018.18.547

M3 - Article

AN - SCOPUS:85040913629

SN - 1472-2747

VL - 18

SP - 547

EP - 568

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

ER -

Second mod 2 homology of artin groups

Abstract

Keywords

Access to Document

Other files and links

Cite this