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Thom Prospectra for Loopgroup representations

Nitu Kitchloo·Jack Morava
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Abstract

We construct an S^1-equivariant prospectrum that models the Atiyah dual of a free loop space of a manifold. By applying a suitably completed S^1-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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Nitu Kitchloo, Jack Morava. 2004-04-29. Thom Prospectra for Loopgroup representations. https://arxiv.org/abs/math/0404541

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