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arXiv:math/0606381 [math.GT]AbstractReferencesReviewsResources

A 1-parameter approach to links in a solid torus

T. Fiedler, V. Kurlin

Published 2006-06-15, updated 2008-10-23Version 3

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.

Comments: 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
Categories: math.GT
Subjects: 57R45, 57M25, 53A04
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