Chris Duston's talk on this starts at minute 43 of this video: http://pirsa.org/13070085 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 S3 and the 3d SPHERE is often denoted S3, so we have a near dog-pile of notation here, but it's really not hard to keep track of it. With the extra S3 group label on the edges the whole previous spin network stuff still goes thru, according to Duston.