Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Comparing 2-handle additions to a genus 2 boundary component   We prove that knots obtained by attaching a band to a split link satisfy the
cabling conjecture. We also give new proofs that unknotting number one knots
are prime and that genus is superadditive under band sum. Additionally, we
prove a collection of results comparing two 2-handle additions to a genus two
boundary component of a compact, orientable 3-manifold. These results give a
near complete solution to a conjecture of Scharlemann and provide evidence for
a conjecture of Scharlemann and Wu. The proofs make use of a new theorem
concerning the effects of attaching a 2-handle to a suture in the boundary of a
sutured manifold.

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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph