The Witten genus and equivariant elliptic cohomology
arXiv:math/0008192
Abstract
We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of the Witten genus, which exhibits a close relationship to recent work on non-equivariant orientations of elliptic spectra.
22 pages. Added section on example of virtual bundles over a point