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

2 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

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10.2140/agt.2018.18.547

Cite this

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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",

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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.

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KW - Coxeter groups

KW - Group cohomology

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DO - 10.2140/agt.2018.18.547

M3 - Article

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EP - 568

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 1

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Second mod 2 homology of artin groups

Abstract

Keywords

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