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If you download the slides PDF first, Chris' slides start at 49/89 of the way, about half way down the PDF file side-rail slide. So you can get to his slides quickly.

On the video it takes a little longer---you can speed things up by nudging the buffering a couple of times. If you nudge the buffering you can get to minute 43 in about 4 or 5 minutes.

this is work co-authored with the splendid Caltech mathematician Matilde Marcolli.

By Alexander's theorem (1920) a spin network can determine the topology of the 3D space, if it simply has some extra edge-labels that refer to the permutation group on 3 letters, a cute kindergarten group with 6 elements. The permutation group on 3 letters is usually denoted S

_{3}and the 3d SPHERE is often denoted

**S**

^{3}, so we have a near dog-pile of notation here, but it's really not hard to keep track of it.

With the extra S

_{3}group label on the edges the whole previous spin network stuff still goes thru, according to Duston.