Thom Prospectra for Loopgroup representations

2004/04/29 by Nitu Kitchloo, Kitchloo, Nitu, Jack Morava +1
Mathematics · #22E6 #55N34 #55P35 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:22E6 #msc:55N34 #msc:55P35

paper · pdf · doi:10.48550/arxiv.math/0404541

arxiv created 2004/04/29 · arxiv updated 2009/12/01

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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