Batalin Vilkovisky algebras and string homology

John Jones (University of Warwick)

Monday 9th March, 2009 16:00-17:00 Mathematics Building, room 204


String homology was introduced by Moira Chas and Dennis Sullivan in 1999. Their idea was to do intersection theory on the loop space of a finite dimensional manifold. In a subsequent paper, published in 2002, Ralph Cohen and myself gave a different approach to the theory using the general methods of algebraic topology and homotopy theory. One of the outputs of string homology is that the theory shows how to associate an algebraic structure known as a Batalin Vilkovisky algebra to a closed finite dimensional manifold. In this talk I will discuss Batalin Vilkovisky algebras and how they arise in algebraic topology, in particular in string homology, and emphasize two fundamental problems. 1. How does one calculate string homology? 2. What exactly does string homology depend on?

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