A 1-parameter approach to links in a solid torus

Fiedler, T.; Kurlin, V.

doi:10.2969/jmsj/06210167

A 1-parameter approach to links in a solid torus

Fiedler, T.; Kurlin, V.

Authors

T. Fiedler

V. Kurlin

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.

Citation

Fiedler, T., & Kurlin, V. (2010). A 1-parameter approach to links in a solid torus. Journal of the Mathematical Society of Japan, 62(1), 167-211. https://doi.org/10.2969/jmsj/06210167

Journal Article Type	Article
Publication Date	Jan 1, 2010
Deposit Date	Dec 7, 2010
Publicly Available Date	Apr 5, 2013
Journal	Journal of the Mathematical Society of Japan.
Print ISSN	0025-5645
Publisher	Mathematical Society of Japan
Peer Reviewed	Peer Reviewed
Volume	62
Issue	1
Pages	167-211
DOI	https://doi.org/10.2969/jmsj/06210167
Keywords	Knot, Braid, Singularity, Bifurcation diagram, Trace graph, Diagram surface, Canonical loop, Trihedral move, Tetrahedral move.