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String topology & compactified moduli space of Riemann surfacesGeometry/Topology
|Start time:||Wed, Oct 6 2010, 4:10PM|
Our goal is to describe the algebraic structure of the homology of the loop space of a manifold. We would like do so by solving the master equation in a chain complex computing the homology. We present a solution to a related equation with an extra term, describe how to eliminate the extra term in one example and suggest a method for eliminating it in general. The solution uses string topology and a compactification of the moduli space of Riemann surfaces. We also present a smaller compactifcation of moduli space over which the string topology construction conjecturally extends.