Loop space homology, string homology, and closed geodesics

Thursday, September 18, 2014 -
3:00pm to 4:00pm
The homology of free loop space of a manifold enjoys additional structure first identified by Chas and Sullivan. The string multiplication has been studied by Ralph Cohen and John Jones and together with J.~Yan, they have introduced a spectral sequence converging to string homology that is related to the Serre spectral sequence for the free loop space. Using this tool, and the work of Felix, Halperin, Lemaire and Thomas, Jones and I establish some conditions on manifolds that guarantee the existence of infinitely many closed geodesics on the manifold in any Riemannian metric. 
Speaker: 
John McCleary
Vassar College
Event Location: 
Fine Hall 214