Ricci Curvature and Fundamental Groups in Riemannian Manifolds - Lecture 3

Explore fundamental concepts in geometric topology through this advanced mathematics lecture focusing on the relationship between Ricci curvature and fundamental groups of complete Riemannian manifolds. Delve into key restrictions discovered since the 1940s, examining their optimality through various topics including polynomial growth, virtual nilpotency, and local uniform finite generation. Learn about motivating examples, methods for proving finite generation of fundamental groups such as Gromov's short generators and Sormani's linear growth theorem, and study spaces with infinitely generated fundamental groups. Master gluing constructions that preserve nonnegative Ricci curvature and analyze counterexamples to the Milnor conjecture in this hour-long exploration of geometric topology.