A minimal geodesic on a Riemannian manifold is a geodesic line that lifts to a globally isometric geodesic line on the universal covering. Bangert proved that there is a lower bound for the number of geometrically distinct minimal geodesics of closed Riemannian manifolds that is linear in the first Betti number, using the stable norm ball on the first homology. We refine this method to obtain a quadratic lower bound. This is based on joint work with Bernd Ammann (Regensburg).
Alle 14.30, Keegan Boyle (University of British Columbia) parlerà di "Alexander polynomials and symmetric knots". Di seguito l'abstract.
In this talk I will discuss the extra topological information which can be extracted from the Alexander polynomial of a knot in S^3 in the case where there are certain types of symmetry on the knot. Specifically, I will discuss 2-periodic, strongly invertible, and strongly negative amphichiral knots. I will mention join work with Ahmad Issa, with Wenzhao Chen, and with Nicholas Rouse and Ben Williams.