Agol, Ian; Hass, Joel; Thurston, William 3-manifold knot genus is NP-complete. (English) Zbl 1192.68305 Proceedings of the thirty-fourth annual ACM symposium on theory of computing (STOC 2002), Montreal, Quebec, Canada, May 19–21, 2002. New York, NY: ACM Press (ISBN 1-581-13495-9). 761-766, electronic only (2002). For the entire collection see [Zbl 1074.68502]. Cited in 2 ReviewsCited in 9 Documents MSC: 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) 57M25 Knots and links in the \(3\)-sphere (MSC2010) × Cite Format Result Cite Review PDF Full Text: DOI References: [1] M. Garey and D. Johnson. Computers and intractability. A guide to the theory of NP-completeness. W. H. Freeman and Co., San Francisco, 1979. · Zbl 0411.68039 [2] W. Haken. Theorie der normalflachen: Ein isotopiekriterium fur den kreisknoten. Acta (MATH)., 105:245-375, 1961. · Zbl 0100.19402 [3] J. H. I. Agol and W. Thurston. The complexity of knot genus. in preparation, 2002. [4] J. C. L. J. Hass and N. Pippenger. The computational complexity of knot and link problems. Journal of the ACM, 46:185-211, 1999. 10.1145/301970.301971 · Zbl 1065.68667 [5] W. Jaco and U. Oertel. An algorithm to decide if a 3-manifold is a haken manifold. Topology, 23:195-209, 1984. · Zbl 0545.57003 [6] W. Jaco and J. H. Rubinstein. Pl equivariant surgery and invariant decompositions of 3-manifolds. Advances in (MATH)., 73:149-191, 1989. · Zbl 0682.57005 [7] W. Jaco and J. L. Tollefson. Algorithms for the complete decomposition of a closed 3-manifold. Illinois J. (MATH)., 39:358-406, 1995. · Zbl 0858.57018 [8] H. Kneser. Geschlossene flachen in dreidimensionalen mannigfaltigkeiten. Jahresbericht (MATH). Verein., 28:248-260, 1929. · JFM 55.0311.03 [9] T. Schaefer. The complexity of satisfiability problems. In Proc 10th Ann. ACM. Symp. on Theory of Computing, pages 216-226. ACM, 1978. 10.1145/800133.804350 · Zbl 1282.68143 [10] A. Schrijver. Theory of Linear and Integer Programming. John Wiley and Sons, Chichester, 1986. · Zbl 0665.90063 [11] H. Schubert. Bestimmung der primfaktorzerlegung von verkettungen. (MATH). Zeitschr., 76:116-148, 1961. · Zbl 0097.16302 [12] H. Seifert. Uber das geschlecht von knoten. (MATH). Annalen, 76:571-592, 1961. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.