Introduction to metric and comparison geometry
- Geometry Topology Working Seminar
- Friday, February 13, 2009 - 15:00 for 1 hour (actually 50 minutes)
- Skiles 269
- Igor Belegradek – School of Mathematics, Georgia Tech
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. In the first (2 hour) lecture I shall explain what volume comparison is and derive several applications.