# Basic String Topology

Thursday, November 9, 2017 -

3:00pm to 4:00pm

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, and a lift of the coproduct from relative to absolute homology. 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.

Speaker:

Nancy Hingston

The College of New Jersey

Event Location:

Fine Hall 110