Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A kernel of a braid group representation yields a knot with trivial knot
  polynomials   We show that a non-trivial, non-central normal subgroup of the braid groups
contains a braid whose closure is a hyperbolic knot with arbitrary large genus.
This shows that non-faithfulness of a quantum representation implies that the
corresponding quantum invariant fails to detect the unknot. The proof utilizes
the Dehornoy ordering of the braid groups.

18
The categories of this paper are: econ
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys