K(π,1) conjecture for Artin groups

2012/11/30 by Paris, Luis
#Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1211.7339

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.

Related

• The K(π,1)-conjecture implies the center conjecture for Artin groups
• The dual approach to the K(π, 1) conjecture
• Introduction to stability conditions and its relation to the K(π,1) conjecture for Artin groups
• Labeled four cycles and the K(π,1)-conjecture for Artin groups
• K(π, 1)'s for Artin groups of finite type