Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Width is not additive   We develop a construction suggested by Scharlemann and Thompson to obtain an
infinite family of pairs of knots $K_{\alpha}$ and $K'_{\alpha}$ so that
$w(K_{\alpha} # K'_{\alpha})=max{w(K_{\alpha}), w(K'_{\alpha})}$. This is the
first known example of a pair of knots such that $w(K#K')<w(K)+w(K')-2$ and it
establishes that the lower bound $w(K#K')\geq max{w(K),w(K')}$ obtained by
Scharlemann and Schultens is best possible. Furthermore, the knots $K_{\alpha}$
provide an example of knots where the number of critical points for the knot in
thin position is greater than the number of critical points for the knot in
bridge position.

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom