Workshop on Geometric Functionals: Analysis and Applications

Abstract: Let M be a compact Riemannian manifold. Morse theory for the energy function on the free loopspace LM of M gives a link between geometry and topology, between the growth of the index of the iterates of closed geodesics on M, and the algebraic structure given by the Chas-Sullivan product on the homology of LM. I will discuss this link, and a new geometric property of the loop coproduct: the nonvanishing of the kth iterate of the coproduct on a homology class ensures the existence of a loop with a (k+1)-fold intersection in every representative of the class. No knowledge of loop products will be assumed. Joint work with Nathalie Wahl.