The $K(\pi,1)$ conjecture for a class of Artin groups

Graham J. Ellis; Emil Sköldberg

doi:10.13025/24786

The $K(\pi,1)$ conjecture for a class of Artin groups

Graham J. Ellis
, Emil Sköldberg

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

15 Citations (Scopus)

Abstract

Salvetti constructed a cellular space B_D for any Artin group A_D defined by a Coxeter graph D. We show that B_D is an Eilenberg-Mac Lane space if B_D′ is an Eilenberg-Mac Lane space for every subgraph D′ of D involving no ∞-edges.

Original language	English (Ireland)
Pages (from-to)	409-415
Number of pages	6
Journal	Comment. Math. Helv.
Volume	85
Issue number	2
DOIs	https://doi.org/10.13025/24786 https://doi.org/10.4171/cmh/200
Publication status	Published - 1 Jan 2010

Keywords

Artin group
Cohomology groups
Eilenberg-Mac Lane space

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10.13025/24786Licence: CC BY-NC-ND
10.4171/cmh/200

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title = "The \$K(\textbackslash{}pi,1)\$ conjecture for a class of Artin groups",

abstract = "Salvetti constructed a cellular space BD for any Artin group AD defined by a Coxeter graph D. We show that BD is an Eilenberg-Mac Lane space if BD′ is an Eilenberg-Mac Lane space for every subgraph D′ of D involving no ∞-edges.",

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AU - Sköldberg, Emil

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N2 - Salvetti constructed a cellular space BD for any Artin group AD defined by a Coxeter graph D. We show that BD is an Eilenberg-Mac Lane space if BD′ is an Eilenberg-Mac Lane space for every subgraph D′ of D involving no ∞-edges.

AB - Salvetti constructed a cellular space BD for any Artin group AD defined by a Coxeter graph D. We show that BD is an Eilenberg-Mac Lane space if BD′ is an Eilenberg-Mac Lane space for every subgraph D′ of D involving no ∞-edges.

KW - Artin group

KW - Cohomology groups

KW - Eilenberg-Mac Lane space

UR - http://hdl.handle.net/10379/11360

UR - https://www.scopus.com/pages/publications/77649210914

U2 - 10.13025/24786

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JO - Comment. Math. Helv.

JF - Comment. Math. Helv.

IS - 2

ER -

The $K(\pi,1)$ conjecture for a class of Artin groups

Abstract

Keywords

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