Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Knottedness is in NP, modulo GRH   Given a tame knot K presented in the form of a knot diagram, we show that the
problem of determining whether K is knotted is in the complexity class NP,
assuming the generalized Riemann hypothesis (GRH). In other words, there exists
a polynomial-length certificate that can be verified in polynomial time to
prove that K is non-trivial. GRH is not needed to believe the certificate, but
only to find a short certificate. This result complements the result of Hass,
Lagarias, and Pippenger that unknottedness is in NP. Our proof is a corollary
of major results of others in algebraic geometry and geometric topology.

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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: atom-ph