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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).

Rambler's Top100