Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterisation of alternating knot exteriors   We give a topological characterisation of alternating knot exteriors based on
the presence of special spanning surfaces. This shows that alternating is a
topological property of the knot exterior and not just a property of diagrams,
answering an old question of Fox. We also give a characterisation of
alternating link exteriors which have marked meridians. We then describe a
normal surface algorithm which can decide if a knot is prime and alternating
given a triangulation of its exterior as input.

7
The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
25
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: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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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: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: stat