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.
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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3004876 |