Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knots with unknotting number one and Heegaard Floer homology   We use Heegaard Floer homology to give obstructions to unknotting a knot with
a single crossing change. These restrictions are particularly useful in the
case where the knot in question is alternating. As an example, we use them to
classify all knots with crossing number less than or equal to nine and
unknotting number equal to one. We also classify alternating knots with ten
crossings and unknotting number equal to one.

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The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: stat
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat