Topology Seminar for 10/17/2002

Nancy Hingston
The College of New Jersey

What can one say about the simple closed geodesics on a 2-sphere with a fixed, generic metric? Easy examples show the lengths may not be bounded. Is the Morse index bounded? We prove some results for metrics satisfying a Kupka-Smale-type condition, and describe examples of metrics whose simple closed geodesics are "not so simple". These include a metric for which the Morse index is unbounded. (joint work with Toby Colding)