Thom Prospectra for Loopgroup representations
Abstract
We construct an S1-equivariant prospectrum that models the Atiyah dual of a free loop space of a manifold. By applying a suitably completed S1-equivariant K-theory to the Atiyah dual, we show how to recover the Witten genus of the manifold. The main technical tool is a Tits building for the loop group. We use this building to construct a dualizing spectrum for the loop group and relate it to work of Freed, Hopkins and Teleman.
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