Recognizing trace graphs of closed braids

Details Recognizing trace graphs of closed braids Recognizing trace graphs of closed braids

2008-08-20

arxiv.org/abs/0808.2713v1

Mathematics

Geometric Topology

20 pages, 15 figures

Scientific paper

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 tetraherdal 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.

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