Alex Oancea will talk in the geometry seminar at 2pm on 29/11/2022. Alex’s title is “Loop product and coproduct in symplectic topology and string topology” and his abstract is below.
I will describe a new algebraic structure, called unital infinitesimal anti-symmetric bialgebra, on the homology of the free loop space of a manifold, respectively on the symplectic homology of a certain class of Weinstein domains. The product is given by the loop product, respectively by the pair of pants product in Floer homology. The coproduct is given by an extension of the Sullivan-Goresky-Hingston coproduct, respectively by an extension of a secondary pair of pants coproduct. As an application I will show how, in certain situations, knowledge of the product allows to compute the coproduct, and vice-versa. The talk will be based on joint work with Kai Cieliebak and Nancy Hingston.