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String topology & compactified moduli space of Riemann surfaces
Geometry/Topology| Speaker: | Kate Poirier |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 6 2010, 4:10PM |
Description
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.