Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kauffman bracket skein module of the handlebody of genus 2 via
  braids   In this paper we present two new bases, $B^{\prime}_{H_2}$ and
$\mathcal{B}_{H_2}$, for the Kauffman bracket skein module of the handlebody of
genus 2 $H_2$, KBSM($H_2$). We start from the well-known Przytycki-basis of
KBSM($H_2$), $B_{H_2}$, and using the technique of parting we present elements
in $B_{H_2}$ in open braid form. We define an ordering relation on an augmented
set $L$ consisting of monomials of all different "loopings" in $H_2$, that
contains the sets $B_{H_2}$, $B^{\prime}_{H_2}$ and $\mathcal{B}_{H_2}$ as
proper subsets. Using the Kauffman bracket skein relation we relate $B_{H_2}$
to the sets $B^{\prime}_{H_2}$ and $\mathcal{B}_{H_2}$ via a lower triangular
infinite matrix with invertible elements in the diagonal. The basis
$B^{\prime}_{H_2}$ is an intermediate step in order to reach at elements in
$\mathcal{B}_{H_2}$ that have no crossings on the level of braids, and in that
sense, $\mathcal{B}_{H_2}$ is a more natural basis of KBSM($H_2$). Moreover,
this basis is appropriate in order to compute Kauffman bracket skein modules of
c.c.o. 3-manifolds $M$ that are obtained from $H_2$ by surgery, since isotopy
moves in $M$ are naturally described by elements in $\mathcal{B}_{H_2}$.

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs