On the complexity of torus knot recognition

John A. Baldwin; Steven Sivek

doi:10.1090/tran/7394

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arXiv · 1706.04424

On the complexity of torus knot recognition

John A. Baldwin·Steven Sivek

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Abstract

We show that the problem of recognizing that a knot diagram represents a specific torus knot, or any torus knot at all, is in the complexity class ${\sf NP} \cap {\sf co\text{-}NP}$, assuming the generalized Riemann hypothesis. We also show that satellite knot detection is in ${\sf NP}$ under the same assumption, and that cabled knot detection and composite knot detection are unconditionally in ${\sf NP}$. Our algorithms are based on recent work of Kuperberg and of Lackenby on detecting knottedness.

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John A. Baldwin, Steven Sivek. 2017-06-14. On the complexity of torus knot recognition. https://doi.org/10.1090/tran/7394

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