Loop Products and Self-Intersections
Connections for Women: Hamiltonian Systems, from topology to applications through analysis August 16, 2018 - August 17, 2018
Location: MSRI: Simons Auditorium
Let M be a compact, oriented manifold and LM the space of maps of the circle into M, the free loop space of M. I will give simplified, chain-level definitions for the Chas-Sullivan "loop" product and coproduct on the homology of LM. Interactions between the product and coproduct will be discussed. I will describe a new link between geometry and the loop coproduct: If a homology class X on LM has a representative with no self-intersections of order >k, then the k-fold coproduct of X is trivial. This result is sharp for spheres and projective spaces. Joint work with Nathalie Wahl. No knowledge of loop products or string topology will be assumed.
Please report video problems to firstname.lastname@example.org.
See more of our Streaming videos on our main VMath Videos page.