Seminar Geometric Group Theory -- Metrics on the knot concordance space

11/25/2015 - 15:00
11/25/2015 - 16:00
Mark Powell (UQAM)
Burnside Hall, Rm. 920 (McGill University)

The slice genus of a knot is the minimal genus of a smoothly embedded surface in the 4-ball whose boundary is the knot. This can be used to define an integer valued metric on the space of knots up to concordance. I will describe a refinement of this that uses a 2-complex construction called a grope (roughly, a grope is tower of embedded surfaces) to better approximate a slice disc, leading to a rational valued metric that refines the slice genus metric and reveals non-discrete behaviour.

Last edited by on Mon, 11/23/2015 - 17:26