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Salvetti complex, spectral sequences and cohomology of Artin groups
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 267-296.

The aim of this short survey is to give a quick introduction to the Salvetti complex as a tool for the study of the cohomology of Artin groups. In particular we show how a spectral sequence induced by a filtration on the complex provides a very natural and useful method to study recursively the cohomology of Artin groups, simplifying many computations. In the last section some examples of applications are presented.

Le but de ce travail est de donner une brève introduction aux complexes de Salvetti comme instrument pour étudier la cohomologie des groupes d’Artin. Nous montrons comment une suite spectrale donnée par une filtration sur le complexe va définir une méthode, utile ainsi que très naturelle, pour étudier récursivement la cohomologie des groupes d’Artin, avec une grande simplification dans les calculs. Dans la dernière partie du travail nous présentons des exemples d’applications.

Published online:
DOI: 10.5802/afst.1407
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     author = {Filippo Callegaro},
     title = {Salvetti complex, spectral sequences  and cohomology of {Artin} groups},
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     publisher = {Universit\'e Paul Sabatier, Toulouse},
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Filippo Callegaro. Salvetti complex, spectral sequences  and cohomology of Artin groups. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 23 (2014) no. 2, pp. 267-296. doi : 10.5802/afst.1407. https://afst.centre-mersenne.org/articles/10.5802/afst.1407/

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