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Room P3.10, Mathematics Building
Nitu Kitchloo, Johns Hopkins University
Atiyah dual of a loop space and the Witten Genus
We construct an equivariant pro-object that represents Poincare Duality for the infinite dimensional manifold LM given by the space of loops on a smooth manifold M. By applying a suitably completed K-theory to this object, we get the structure of a TQFT (or Frobenius algebra) which has the value on the surface of genus zero given by the Witten genus of M.