The efficient certification of knottedness and Thurston norm
Geometric Topology
2021-04-13 v3
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 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.
Cite
@article{arxiv.1604.00290,
title = {The efficient certification of knottedness and Thurston norm},
author = {Marc Lackenby},
journal= {arXiv preprint arXiv:1604.00290},
year = {2021}
}
Comments
104 pages, 24 figures; v3 is the final version, to appear in Advances in Mathematics