Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The almost alternating diagrams of the trivial knot   Bankwitz characterized an alternating diagram representing the trivial knot.
A non-alternating diagram is called almost alternating if one crossing change
makes the diagram alternating. We characterize an almost alternaing diagram
representing the trivial knot. As a corollary we determine an unknotting number
one alternating knot with a property that the unknotting operation can be done
on its alternating diagram.

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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph