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The efficient certification of knottedness and Thurston norm
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We show that the problem of determining whether a knot in the 3-sphere is non-trivial lies in NP. This is a consequence of the following more general result. The problem of determining whether the Thurston norm of a second homology class in a compact orientable 3-manifold is equal to a given integer is in NP. As a corollary, the problem of determining the genus of a knot in the 3-sphere is in NP. We also show that the problem of determining whether a compact orientable 3-manifold has incompressible boundary is in NP.
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Cited by 1 Pith paper
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Link Crossing Number is NP-hard
Determining the minimum crossing number of a link is NP-hard, via a reduction from the bipartite crossing number problem.
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