A theorem of Gromov states that the number of generators of the fundamental group of a manifold with nonnegative
curvature is bounded by a constant which only depends on the dimension of the manifold. The main ingredient
in the proof is Toponogov’s theorem, which roughly speaking says that the triangles on spaces with positive
curvature, such as spheres, are thick compared to triangles in the Euclidean plane. In the talk I shall explain
this more carefully and deduce Gromov’s result.
- Junior Geometry and Topology Seminar