Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twist Number and the Alternating Volume of Knots   It was previously shown by the second author that every knot in $S^3$ is
ambient isotopic to one component of a two-component, alternating, hyperbolic
link. In this paper, we define the alternating volume of a knot $K$ to be the
minimum volume of any link $L$ in a natural class of alternating, hyperbolic
links such that $K$ is ambient isotopic to a component of $L$. Our main result
shows that the alternating volume of a knot is coarsely equivalent to the twist
number of a knot.

8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: physics
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an