Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free genus one knots with large volume   A Seifert surface F for a knot K is free if the complement of F is a
handlebody (i.e., has free fundamental group). The free genus of K is the
minimum genus among all free Seifert surfaces for K. In this paper we show that
there exist families of hyperbolic knots with arbitrarily large volume, which
each have free genus one. This implies that there are knots with free genus one
but arbitrarily large canonical genus, and that there exist knots admitting
incompressible free Seifert surfaces which cannot be built by applying
Seifert's algorithm to a projection of the knot.

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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat