Representations of the braid group by automorphisms of groups, invariants of links, and Garside groups
| dc.creator | Crisp, John | |
| dc.creator | Paris, Luis | |
| dc.date | 2002-12-10 | |
| dc.date.accessioned | 2026-07-07T04:53:40Z | |
| dc.date.available | 2026-07-07T04:53:40Z | |
| dc.description | From a group $H$ and a non-trivial element $h$ of $H$, we define a representation $ρ: B_n \to \Aut(G)$, where $B_n$ denotes the braid group on $n$ strands, and $G$ denotes the free product of $n$ copies of $H$. Such a representation shall be called the Artin type representation associated to the pair $(H,h)$. The goal of the present paper is to study different aspects of these representations. Firstly, we associate to each braid $β$ a group $Γ_{(H,h)} (β)$ and prove that the operator $Γ_{(H,h)}$ determines a group invariant of oriented links. We then give a topological construction of the Artin type representations and of the link invariant $Γ_{(H,h)}$, and we prove that the Artin type representations are faithful. The last part of the paper is dedicated to the study of some semidirect products $G \rtimes_ρB_n$, where $ρ: B_n \to \Aut(G)$ is an Artin type representation. In particular, we show that $G \rtimes_ρB_n$ is a Garside group if $H$ is a Garside group and $h$ is a Garside element of $H$. | |
| dc.identifier | https://arxiv.org/abs/math/0212138 | |
| dc.identifier | http://arxiv.org/abs/math/0212138 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65942 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F36; 57M27 | |
| dc.title | Representations of the braid group by automorphisms of groups, invariants of links, and Garside groups | |
| dc.type | text |