On the welded Tube map

Benjamin Audoux (1)

1 I2M - Institut de Mathématiques de Marseille

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.

Keywords: welded knots; ribbon 2--knots; Tube map

Domains: Geometric Topology [math.GT]

Benjamin Audoux. On the welded Tube map. Knot theory and its applications. ICTS program knot theory and its applications (KTH-2013), IISER Mohali, India, December 10--20, 2013, 2016, ⟨10.1090/conm/670/13457⟩. ⟨hal-01066617⟩