Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cabling Conjecture for Small Bridge Number   Let $k\subset S^3$ be a nontrivial knot. The Cabling Conjecture of Francisco
Gonz\'alez-Acu\~na and Hamish Short posits that $\pi$-Dehn surgery on $k$
produces a reducible manifold if and only if $k$ is a $(p,q)$-cable knot and
the surgery slope $\pi$ equals $pq$. We extend the work of James Allen Hoffman
to prove the Cabling Conjecture for knots with bridge number up to $5$.

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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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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: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg