On the welded Tube map

Abstract

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.

23 pages ; v2: an error corrected and stylistic modifications ; to appear in Contemporary Mathematics

References in corpus (2)

• Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander Polynomial
• Homotopy classification of ribbon tubes and welded string links

Cited by in corpus (1)

• Virtually Symmetric representations and marked Gauss diagrams