USA Topology Seminar
Cell decompositions of knot complements and presentations of π
Scott Carter, USA
Thursday, September 16, 2010
It is well-known that both the Wirtinger and the Dehn presentations are obtained by decomposing a knot complement as handle decomposition with 0, 1 and 2-handles. Not so well known is the process of turning the handle decomposition for the Dehn presentation upside-down. I will show how to do this and thereby how to get a presentation for π
which is quite interesting. I'll show a few examples, and if I am lucky between now and then, I'll try and work out a presentation of 8
. I think the resulting relations explain Dan and Susan's conventions for vertex colorings.