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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?

flag	asked Dec 13 at 0:59 Ryan Budney 4,149●5●25

Scott Carter · Accepted Answer · 2009-12-13 02:01:15Z UTC

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.

Ryan Budney · Answer 2 · 2009-12-13 22:46:32Z UTC

2

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tada: link text

answered Dec 13 at 22:46

Ryan Budney
4,149●5●25

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Very pretty indeed! – Sam Nead Dec 13 at 23:31

Scott Morrison · Answer 3 · 2009-12-13 18:50:05Z UTC

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The Knot Atlas seems like it would be a good home for ribbon diagrams. At present, it has exactly one: for the knot 6₁.

The Knot Atlas is a wiki, it's user editable, and you can even upload new images.

answered Dec 13 at 18:50

Scott Morrison♦
2,887●8●28

I'd be happy to do that but editing that wiki appears very complicated as everything is auto-generated -- using the "edit" link would likely mean my edit would be auto-erased the next time the page is generated? – Ryan Budney Dec 13 at 21:05

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It is a bit evil. The right thing to do is to find the link [edit Notes for 6_1's three dimensional invariants]. That takes you to a sub-page which is not automatically generated, but which is 'transcluded' into the main page for 6_1. – Scott Morrison♦ Dec 13 at 22:20

Okidokie, I think I may have done the right thing. ? – Ryan Budney Dec 13 at 22:38

Generating ribbon diagrams for knots known to be ribbon knots

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