[Math] Generating ribbon diagrams for knots known to be ribbon knots

gt.geometric-topologyknot-theory

Is there a source in the literature for ribbon diagrams for the knot-table knots known to be ribbon knots?

For example, I'm interested in doing a computation which needs as input a ribbon diagram for the knot $8_{20}$ (Rolfsen knot table notation). This knot is known to be ribbon, but I don't know a ribbon diagram for the knot.

Usually when I encounter a claim of the sort "knot X is ribbon" either the author supplies the ribbon diagram, or nothing. Citations to information of this sort seem kind of sparse. Or am I just unaware of a standard source for this type of information?

Best Answer

I think Kawauchi's book has tables that include ribbon diagrams, but I don't have a copy with me. Look at Livingston and Cha . It is not hard to get a ribbon disk from this diagram: add a handle between the ears on the top and bottom right.

Generally, I check Livingston/Cha , Bar-Natan, and Saito for various information.

@ears: there are a pair of symmetric clasps on the top and bottom of the diagram. Pull the top-most and bottom-most arc to the right, and then attach a band. The vertical arc that forms a triangle, and the right vertical arc from the band forms an obvious embedded circle.

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