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