On the welded Tube map Auteur(s): Audoux B.
Ref HAL: hal-01066617_v1 Ref Arxiv: 1408.5479 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: This note investigates the so-called Tube map which connects welded knots, that is a quotient of the virtual knot theory, to ribbon torus-knots, that is a restricted notion of fillable knotted tori in the 4-sphere. It emphasizes the fact that ribbon torus-knots with a given filling are in one-to-one correspondence with welded knots before quotient under classical Reidemeister moves and reformulates these moves and the known sources of non-injectivity of the Tube map in terms of filling changes. Commentaires: 23 pagesv2 : an error corrected and stylistic modifications |