$K(\pi ,1)$ conjecture for Artin groups

Luis Paris

doi:10.5802/afst.1411

K (π, 1)

conjecture for Artin groups

Luis Paris

Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 361-415.

Abstract
Abstract

The purpose of this paper is to put together a large amount of results on the $K (π, 1)$ conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as self-contained as possible.

Le but de cet article est de mettre ensemble une grande partie des résultats connus sur la conjecture du $K (π, 1)$ pour les groupes d’Artin et de les rendre accessibles aux non-spécialistes. Tout d’abord, ce texte est un exposé, contenant les définitions de base, les principaux résultats, des exemples et un aperçu historique. C’est aussi un texte qui devrait servir de référence dans le sujet et qui contient des démonstrations de la plupart des résultats énoncés. Certaines démonstrations et quelques résultats sont nouveaux. En outre, le texte, s’adressant à des non-spécialistes, est aussi complet que possible.

MR Zbl

DOI: 10.5802/afst.1411

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     author = {Luis Paris},
     title = {$K(\pi ,1)$ conjecture for {Artin} groups},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {361--415},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 23},
     number = {2},
     year = {2014},
     doi = {10.5802/afst.1411},
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     zbl = {06297897},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1411/}
}

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Luis Paris. $K(\pi ,1)$ conjecture for Artin groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 361-415. doi : 10.5802/afst.1411. https://afst.centre-mersenne.org/articles/10.5802/afst.1411/

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