Knot Theory and Its Applications [book]

Krishnendu Gongopadhyay, Rama Mishra
2016 Contemporary Mathematics  
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.
doi:10.1090/conm/670 fatcat:3ij2y5aimrg4jojdkefoymooqi