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January, 2010 A 1-parameter approach to links in a solid torus
Thomas FIEDLER, Vitaliy KURLIN
J. Math. Soc. Japan 62(1): 167-211 (January, 2010). DOI: 10.2969/jmsj/06210167


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.


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Thomas FIEDLER. Vitaliy KURLIN. "A 1-parameter approach to links in a solid torus." J. Math. Soc. Japan 62 (1) 167 - 211, January, 2010.


Published: January, 2010
First available in Project Euclid: 5 February 2010

zbMATH: 1201.57003
MathSciNet: MR2648220
Digital Object Identifier: 10.2969/jmsj/06210167

Primary: 57R45
Secondary: 53A04 , 57M25

Keywords: bifurcation diagram , Braid , canonical loop , diagram surface , knot , singularity , tetrahedral move , trace graph , trihedral move

Rights: Copyright © 2010 Mathematical Society of Japan


Vol.62 • No. 1 • January, 2010
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