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.

[img] Text
1parameter-knots.pdf - Author Accepted Manuscript

Download (1MB)

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: 19 Jan 2023 07:24
DOI: 10.2969/jmsj/06210167
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3004876