Journal title
Advances in Mathematics
DOI
10.1016/j.aim.2021.107796
Volume
387
Last updated
2024-04-09T11:34:38.73+01:00
Abstract
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 irreducible 3-manifold with (possibly empty) toroidal boundary 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.
Symplectic ID
614586
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Publication type
Journal Article
Publication date
15 Jun 2021