K ( π , 1 ) conjecture for Artin groups

Luis Paris

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 2, page 361-415
  • ISSN: 0240-2963

Abstract

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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.

How to cite

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Paris, Luis. "$K(\pi ,1)$ conjecture for Artin groups." Annales de la faculté des sciences de Toulouse Mathématiques 23.2 (2014): 361-415. <http://eudml.org/doc/275390>.

@article{Paris2014,
abstract = {The purpose of this paper is to put together a large amount of results on the $K(\pi ,1)$ 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.},
author = {Paris, Luis},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {Artin groups; conjecture; Salvetti complexes; arrangements of hyperplanes; Coxeter groups; reflection groups; Artin monoids; homotopy types; cellular decompositions; fundamental groups},
language = {eng},
month = {3},
number = {2},
pages = {361-415},
publisher = {Université Paul Sabatier, Toulouse},
title = {$K(\pi ,1)$ conjecture for Artin groups},
url = {http://eudml.org/doc/275390},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Paris, Luis
TI - $K(\pi ,1)$ conjecture for Artin groups
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2014/3//
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 2
SP - 361
EP - 415
AB - The purpose of this paper is to put together a large amount of results on the $K(\pi ,1)$ 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.
LA - eng
KW - Artin groups; conjecture; Salvetti complexes; arrangements of hyperplanes; Coxeter groups; reflection groups; Artin monoids; homotopy types; cellular decompositions; fundamental groups
UR - http://eudml.org/doc/275390
ER -

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