Abstract

In knot theory, we use self-repulsive energies as a tool to measure entanglement. In the first half of the talk, I will give a crash-course introduction into self-repulsive energies. I will present some properties, which were used in order to construct a Riemannian metric measuring this self-entanglement. Later, I’m going to introduce infinite dimensional Riemannian geometry and characterize the tangent-spaces of fractional Sobolev-spaces.

In the second half of the talk I will present the metric and sketch the proof of geodesic completeness (i.e. that geodesics w.r.t the metric are defined for all time). Furthermore, some of the occurring problems and how we overcame them will be explained.

This is ongoing work of me and my collaborators, Prof. Philipp Reiter and Dr. Henrik Schumacher.