Hall 123

Curvature and growth of fundamental group

Arghya Mondal

IMSc

Let *M* be a complete Riemannian manifold whose fundamental group is finitely generated. If we fix a finite generating set of a group, then the reduced word length gives a metric on it. Denote the number of group elements in a ball of centre the identity and radius *s* as *y(s)*. The rate of growth of *y(s)* with respect to *s* is called the *growth rate* of the group. There is a connection between curvature of *M* and the rate of growth of it's fundamental group. This will be our topic of discussion. No knowledge of Riemannian geometry will be assumed.