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• CommentRowNumber1.
• CommentAuthorAndrew Stacey
• CommentTimeApr 1st 2011

Expanded Vassiliev invariant, started Kontsevich integral, did a bit of reorganisation on knot theory (in particular, linking to more pages).

In case anyone’s wondering, there was a book put on the arXiv a couple of days ago touting itself as an introduction to Vassiliev invariants. I’m reading through it and taking notes as I go. I left in a bit of a rush today so the formatting of the Kontsevich integral went a bit haywire, and I made a statement on the Vassiliev invariant page that I know I didn’t say quite right.

In the arXiv book, Vassiliev invariants are introduced first using the Vassiliev skein relations, not their “proper” way (which I haven’t gotten to yet so I don’t know it). The formula looked very like a boundary map on a complex, but I think it has to be a cubical complex rather than a simplicial one. Only it isn’t the full boundary map, rather a partial boundary map (going to opposite faces), but I didn’t get it straight in my head until later. But now I think I’m going to wait until I read the bit about the true definition - which I guess will be something like this - before correcting it (unless anyone gets there before me, of course).

Drew a few more SVGs relevant for knots as well. The code for producing the trefoil knot is very nice now, though I say so myself!

• CommentRowNumber2.
• CommentAuthorAndrew Stacey
• CommentTimeApr 11th 2011

Some tidying up at knot group. Also added cinquefoil - SVG (though that’s not quite the one at knot group since the latter is labelled).

• CommentRowNumber3.
• CommentAuthorjim_stasheff
• CommentTimeApr 11th 2011
cinquefoil - SVG

error message said it doesn't exist
• CommentRowNumber4.
• CommentAuthorAndrew Stacey
• CommentTimeApr 11th 2011

Corrected. It was actually cinquefoil knot - SVG that I created, but I’ve added a redirect to cinquefoil - SVG as well.

Thanks.