A 1-parameter approach to links in a solid torus

Fiedler, Thomas and Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2010) A 1-parameter approach to links in a solid torus. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 62 (1). pp. 167-211.

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Abstract

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.

Item Type:	Article
Additional Information:	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
Uncontrolled Keywords:	knot, braid, singularity, bifurcation diagram, trace graph, diagram surface, canonical loop, trihedral move, tetrahedral move
Depositing User:	Symplectic Admin
Date Deposited:	14 Dec 2016 16:24
Last Modified:	14 Mar 2024 17:32
DOI:	10.2969/jmsj/06210167
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3004876