On the welded Tube map

Benjamin Audoux

doi:10.1090/conm/670

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arXiv · 1408.5479

On the welded Tube map

Benjamin Audoux

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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.

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BibTeX RIS

Benjamin Audoux. 2014-08-23. On the welded Tube map. https://doi.org/10.1090/conm/670

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