Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kauffman Bracket Skein Module of the Connected Sum of Handlebodies: A
  Counterexample   In this paper we disprove a twenty-two year old theorem about the structure
of the Kauffman bracket skein module of the connected sum of two handlebodies.
We achieve this by analysing handle slidings on compressing discs in a
handlebody. We find more relations than previously predicted for the Kauffman
bracket skein module of the connected sum of handlebodies, when one of them is
not a solid torus. Additionally, we speculate on the structure of the Kauffman
bracket skein module of the connected sum of two solid tori.

28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
18
The categories of this paper are: econ