The Unapologetic Mathematician

Mathematics for the interested outsider

New result

Never believe anyone who says that drinking never helps anything, for tonight over many a pint o’ Guinness I hit upon the solution to a problem that’s been nagging at me for some time. The answer is so incredibly simple that I’m feeling stupid for not thinking of it before. So here it is:

Cospans in the comma category of quandles over a given quandle Q from the free quandle on m letters to the free quandle on n letters categorify the extension of link colorings by Q to tangles.

This gives me a new marker to aim at. I can explain this, but it will require more preliminaries before it’s really accessible to the GILA (Generally Interested Lay Audience) as yet. Those who know quandles — a topic I’ll be covering early next week — and category theory and some knot theory should be able to piece together the meaning now. For the rest of you.. stay tuned.

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March 17, 2007 - Posted by | Knot theory

1 Comment »

  1. [...] in the Geometry, Symmetry, and Physics seminar here at Yale about the work that spun out of my realization of March 16. This ties into knot colorings, but goes far beyond that starting point. I won’t be able to [...]

    Pingback by Some of my own stuff « The Unapologetic Mathematician | April 26, 2007 | Reply


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