Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High Distance Bridge Surfaces   Given integers b, c, g, and n, we construct a manifold M containing a
c-component link L so that there is a bridge surface Sigma for (M,L) of genus g
that intersects L in 2b points and has distance at least n. More generally,
given two possibly disconnected surfaces S and S', each with some even number
(possibly zero) of marked points, and integers b, c, g, and n, we construct a
compact, orientable manifold M with boundary S \cup S' such that M contains a
c-component tangle T with a bridge surface Sigma of genus g that separates the
boundary of M into S and S', |T \cap Sigma|=2b and T intersects S and S'
exactly in their marked points, and Sigma has distance at least n.

10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph