I gave a talk (to fellow undergraduates in Maths here in Cambridge) about the topology, namely \(\pi_1(M)\) of manifolds with negative sectional curvature. In it, I covered
- Exponential map
- Sectional curvature
- Cartan-Hadamard (no proof)
- Cartan’s theorem about isometries with finite order
- Preissmann’s theorem
- Byers’ theorem (no proof)
- Milnor’s theorem about exponential growth of \(\pi_1(M)\) (no proof)
The notes can be found here. The spaces are for diagrams which I drew in by hand (on paper). The talk mainly followed the following textbooks
- Riemannian Geometry - Petersen
- Riemannian Geometry - do Carmo