Abstract
To a closed braid in a solid torus we associate a trace graph in a thickened torus in such a way that closed braids are isotopic if and only if their trace graphs can be related by trihedral and tetrahedral moves. For closed braids with a fixed number of strands, we recognize trace graphs up to isotopy and trihedral moves in polynomial time with respect to the braid length.
Citation
Thomas Fiedler. Vitaliy Kurlin. "Recognizing trace graphs of closed braids." Osaka J. Math. 47 (4) 885 - 909, December 2010.
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