3-manifold knot genus is NP-complete

Authors:
Ian Agol;Joel Hass;William Thurston
Affiliations:
University of Illinois at Chicago, Chicago, IL;University of California, Davis, CA;University of California, Davis, CA
Venue:
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Year:
2002

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Abstract

We show that the problem of deciding whether a polygonal knot in a closed three-dimensional manifold bounds a surface of genus at most g is NP-complete.