Members Seminar | |

Topic: | Loop Products and Dynamics |

Speaker: | Nancy Hingston |

Affiliation: | The College of New Jersey; Member, School of Mathematics |

Date: | Monday, November 28 |

Time/Room: | 2:00pm - 3:00pm/S-101 |

A 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 on M in the given metric. Morse theory gives a link between Hamiltonian dynamics and the topology of loop spaces, between iteration of closed geodesics and the algebraic structure given by the Chas-Sullivan product on the homology of LM. Geometry reveals the existence of a related product on the cohomology of LM. A number of known results on the existence of closed geodesics are naturally expressed in terms of nilpotence of products. We use products to prove a resonance result for the loop homology of spheres. I will not assume any prior knowledge of loop products. Mark Goresky, Hans-Bert Rademacher, and (work in progress) Ralph Cohen and Nathalie Wahl are collaborators.