Summary: Math 241B
Instructor: Guofang Wei
Winter 20002001
Last quarter we studied the relationship between Ricci curvature and
topology. The basic tools were:
1. Volume Comparison
2. Laplacian Comparison
3. Excess Estimate
This quarter we study the relationship between sectional curvature and
topology. Our tools will be:
1. Critical Point Theory for Distance Functions
2. Toponogov Comparison
As applications we will have:
1. Generalized Sphere Theorem
2. Soul Theorem
3. Gromov's Betti Number Estimate
4. Homotopy Finiteness Theorem
1
1 Introduction to Critical Point Theory of
Distance Functions
