Resonance for loop homology on spheres

Resonance for loop homology on spheres

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Nancy Hingston , College of New Jersey and IAS
IAS - Simonyi Hall Seminar Room SH-101

Fix a metric (Riemannian or Finsler) on a compact manifold M. The critical points of the length function on the free loop space LM of M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed geodesics, and the algebraic structure given by the Chas-Sullivan product on the homology of LM and the “dual” loop cohomology product. If X is a homology class on LM, the "minimax" critical level Cr(X) is a critical value of the length function. Gromov proved that if M is simply connected, there are positive constants k and K so that for every homology class X of degree >dim(M) on LM, k·deg(X)