The efficient certification of knottedness and Thurston norm

Author: 

Lackenby, M

Publication Date: 

15 June 2021

Journal: 

Advances in Mathematics

Last Updated: 

2021-10-11T20:54:03.413+01:00

Volume: 

387

DOI: 

10.1016/j.aim.2021.107796

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

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article