A 1-parameter approach to links in a solid torus

FIEDLER, Thomas; KURLIN, Vitaliy

J. Math. Soc. Japan, Tome 62 (2010) no. 1, p. 167-211 / Harvested from Project Euclid

Résumé

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.

Publié le : 2010-01-15
Classification: knot, braid, singularity, bifurcation diagram, trace graph, diagram surface, canonical loop, trihedral move, tetrahedral move, 57R45, 57M25, 53A04

@article{1265380428,
     author = {FIEDLER, Thomas and KURLIN, Vitaliy},
     title = {A 1-parameter approach to links in a solid torus},
     journal = {J. Math. Soc. Japan},
     volume = {62},
     number = {1},
     year = {2010},
     pages = { 167-211},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1265380428}
}

FIEDLER, Thomas; KURLIN, Vitaliy. A 1-parameter approach to links in a solid torus. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp.  167-211. http://gdmltest.u-ga.fr/item/1265380428/