Cornell Math - MATH 757, Fall 2000

MATH 757 — Fall 2000
Topics in Topology: Comparison Geometry

Comparison Geometry studies how metric invariants of a space, especially curvature, determine its topology. While the focus of the course will be Riemannian manifolds, sectional curvature and Ricci curvature, we will also explore how the notion of curvature can be extended to more general metric spaces. Potential topics include Toponogov's theorem, Bishop-Gromov volume comparison, Gromov-Hausdorff convergence, finiteness theorems (for homotopy or diffeomorphism types), critical point theory for the distance function, Alexandrov spaces, sphere theorems, convexity and soul theorems.

Prerequisites: An introduction to Riemannian geometry, 651 and a willingness to accept results from 662 as needed.