Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Additivity of Bridge Number of Knots   We provide a new proof of the following results of H. Schubert: If K is a
satellite knot with companion J and pattern L that lies in a solid torus T in
which it has index k, then the bridge numbers satisfy the following: 1) The
bridge number of K is greater than or equal to the product of k and the bridge
number of J; 2) If K is a composite knot (this is the case k = 1), then the
bridge number of K is one less than the sum of the bridge numbers of J and L.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg