Kissing numbers of manifolds and graphs

Abstract: The kissing number of a metric space X is defined as the number of distinct homotopy classes of shortest closed geodesics in X. We are interested in how large the kissing number can get within certain families of metric spaces. This problem has been studied for flat tori and hyperbolic surfaces before. I will discuss joint work with Bram Petri where we obtain upper bounds for the kissing number of closed hyperbolic manifolds of any dimension and of regular graphs.

Frenchdynamical systemsgeometric topology

Audience: researchers in the topic

Séminaire de géométrie et dynamique