Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Obstructions to trivializing a knot   The recent proof by Bigelow and Krammer that the braid groups are linear
opens the possibility of applications to the study of knots and links. It was
proved by the first author and Menasco that any closed braid representative of
the unknot can be systematically simplified to a round planar circle by a
sequence of exchange moves and reducing moves. In this paper we establish
connections between the faithfulness of the Krammer-Lawrence representation and
the problem of recognizing when the conjugacy class of a closed braid admits an
exchange move or a reducing move.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th