Loop products, closed geodesics and self-intersections

Hingston 2019 03 06

Nancy Hingston
The College of New Jersey
March 6, 2019

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.