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O.V.Schwarzman

Elementary Theory of Curvature in Topology

1. Basic facts about the Metrics, Connections, and Curvature.
2. Geodesics. The Hopf-Rinow theorem.
3. First and second variations.
4. Sec, Ric, and Scal.
5. The Singe theorem.
6. The Hadamard-Cartan theorem.
7. Elementary geometry of the Sec<=0-manifolds. The Toponogov Theorem.
8. The Tits-Karpelevich compactification.
9. SL(n,R)/SO(n,R). An example.
10. Gromov Simplicial Volume and the MinVol problem.
11. Something about Sec>=0-manifolds.
12. Berge spheres.
13. Fundamental group growth and curvature (the Milnor theorem).