arXiv:2004.01471 Abstract | arXiv Analytics

arXiv:2004.01471 [math.GT]Abstract References Reviews Resources

The computational complexity of determining knot genus in a fixed 3-manifold

Published 2020-04-03Version 1

We show that the problem of determining the genus of a knot in a fixed compact, orientable three-dimensional manifold lies in NP. This answers a question asked by Agol, Hass, and Thurston in 2002. Previously, this was known for rational homology three-spheres, by the work of the first author.

Comments: 38 pages, 6 figures

Categories: math.GT

Subjects: 57N10, 57M27, 68Q15, 68Q17, 57M25

Keywords: determining knot genus, computational complexity, rational homology three-spheres, orientable three-dimensional manifold lies, first author

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