Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Alternating links have representativity 2   We prove that if $L$ is a non-trivial alternating link embedded (without
crossings) in a closed surface $F\subset S^3$, then $F$ has a compressing disk
whose boundary intersects $L$ in no more than two points. Moreover, whenever
the surface is incompressible and $\partial$-incompressible in the link
exterior, it can be isotoped to have a standard tube at some crossing of any
reduced alternating diagram.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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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: hep-lat
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: eess