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.
Nancy Hingston
The College of New Jersey
Event Location: 
Fine Hall 110