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

Graham J. Ellis; Emil Sköldberg

doi:10.4171/CMH/200

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

14 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/10.4171/CMH/200
Publication status	Published - 1 Jan 2010

Keywords

Artin group
Cohomology groups
Eilenberg-Mac Lane space

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Ellis, Graham and Sk\"oldberg, Emil

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10.4171/CMH/200

Cite this

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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.",

keywords = "Artin group, Cohomology groups, Eilenberg-Mac Lane space",

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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.

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KW - Cohomology groups

KW - Eilenberg-Mac Lane space

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U2 - 10.4171/CMH/200

DO - 10.4171/CMH/200

M3 - Article

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EP - 415

JO - Comment. Math. Helv.

JF - Comment. Math. Helv.

IS - 2

ER -

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

Abstract

Keywords

Authors (Note for portal: view the doc link for the full list of authors)

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