Braid groups and Artin groups

Abstract

This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a presentation, accessible to non-experts, of various topological and algebraic aspects of these groups. It is also a report on three points of the theory: the faithful linear representations, the cohomology, and the geometrical representations.

References in corpus (10)

• Presentations for the punctured mapping class groups in terms of Artin groups
• The homology of the Milnor fiber for classical braid groups
• Garside categories, periodic loops and cyclic sets
• Garside groups are strongly translation discrete
• A note on the Lawrence-Krammer-Bigelow representation
• Translation numbers in a Garside group are rational with uniformly bounded denominators
• Some power of an element in a Garside group is conjugate to a periodically geodesic element
• Faithfulness of the Lawrence representation of braid groups
• A class of Garside groupoid structures on the pure braid group
• On the cycling operation in braid groups

Cited by in corpus (5)

• Arrangements of Submanifolds and the Tangent Bundle Complement
• Basic results on braid groups
• On PM-monoids and braid PM-monoids
• Linear Configurations of Complete Graphs $K_4$ and $K_5$ in ${\mathbb{R}}^3$, and Higher Dimensional Analogs
• Relative Garside elements of Artin monoids