4/1/2010

Nancy Hingston
College of New Jersey

Resonance for loop homology on spheres

A Riemannian metric on a compact manifold M gives rise to a length function on the free loop space LM, whose critical points are the closed geodesics in the given metric on M. If x is a homology class on LM, the "minimax" critical level cr(x) is a critical value. Let M be a sphere, and fix a metric and a coefficient field. We prove that the limit as deg(x) goes to infinity of cr(x)/deg(x) exists. Mark Goresky and Hans-Bert Rademacher are collaborators.