Affiliation:
1. Mathematical Institute University of Oxford Oxford UK
2. Department of Mathematics King's College London Strand London UK
Abstract
AbstractWe show that the problem of deciding whether a knot in a fixed closed orientable 3‐dimensional manifold bounds a surface of genus at most is in co‐NP. This answers a question of Agol, Hass and Thurston in 2002. Previously, this was known for rational homology 3‐spheres, by the work of the first author.
Reference40 articles.
1. The unsolvability of certain algorithmic problems in the theory of groups;Adian S. I.;Tr. Mosk. Mat. Obs.,1957
2. The computational complexity of knot genus and spanning area
3. Computational Complexity
4. Sylvester's identity and multistep integer‐preserving Gaussian elimination;Bareiss E. H.;Math. Comp.,1968
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