Basic String Topology

Basic String Topology

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Nancy Hingston, The College of New Jersey
Fine Hall 110

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.