Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of the braid group by automorphisms of groups,
  invariants of links, and Garside groups   From a group $H$ and a non-trivial element $h$ of $H$, we define a
representation $\rho: B_n \to \Aut(G)$, 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 $\beta$ a group $\Gamma_{(H,h)} (\beta)$
and prove that the operator $\Gamma_{(H,h)}$ determines a group invariant of
oriented links. We then give a topological construction of the Artin type
representations and of the link invariant $\Gamma_{(H,h)}$, 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 $G \rtimes_\rho B_n$, where
$\rho: B_n \to \Aut(G)$ is an Artin type representation. In particular, we show
that $G \rtimes_\rho B_n$ is a Garside group if $H$ is a Garside group and $h$
is a Garside element of $H$.

14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess