Representations of Braid Groups and Generalisations

2007/03/23 by Valerij G. Bardakov, Bardakov, Valerij G., Paolo Bellingeri +1
Mathematics · #20F10 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Primary 20F36 #Secondary 20F05 #math.GR #msc:20F05 #msc:20F10 #msc:20F36

paper · pdf · doi:10.48550/arxiv.math/0703692

Few misprints corrected, simpler proof for proposition 10

openalex publication_date 2007/03/23 · arxiv created 2007/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of oriented surfaces with boundary components as (outer) automorphisms of free groups. We give also similar representations for braid groups of non oriented surfaces with boundary components and we show a representation of braid groups of closed surfaces as outer automorphisms of free groups. Finally, we provide faithful representations of Artin-Tits groups of type D as automorphisms of free groups.

Related

• Representing braids by automorphisms
• On the Linearized Artin Braid Representation
• Representations of the braid group by automorphisms of groups, invariants of links, and Garside groups
• Introduction to representations of braid groups
• On presentation of Surface Braid Groups