A 1-parameter approach to links in a solid torus
Abstract
Description
To an oriented link in a solid torus we associate a trace graph in a thickened torus in such a way that links are isotopic if and only if their trace graphs can be related by moves of finitely many standard types. The key ingredient is a study of codimension~2 singularities of link diagrams. For closed braids with a fixed number of strands, trace graphs can be recognized up to equivalence excluding one type of moves in polynomial time with respect to the braid length.
38 pages, 14 figures, the applications on closed braids were moved to another paper `Recognising trace graphs of closed braids' (arXiv:0808.2713), more details were added on versal deformations of codimension 2 singularities
38 pages, 14 figures, the applications on closed braids were moved to another paper `Recognising trace graphs of closed braids' (arXiv:0808.2713), more details were added on versal deformations of codimension 2 singularities