Equivariant elliptic cohomology and rigidity

TheWitten genus and equivariant elliptic cohomology

We construct a Thom class in complex equivariant elliptic cohomology extending the equivariant Witten genus. This gives a new proof of the rigidity of theWitten genus, which exhibits a close relationship to recent work on non-equivariant orientations of elliptic spectra.

Rational S 1 - Equivariant Elliptic Cohomology

We give a functorial construction of a rational S 1-equivariant cohomology theory from an elliptic curve equipped with suitable coordinate data. The elliptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology theory on the compactification of an S 1-representation is given by the sheaf cohomology of a suitable line bundle on the curve. The construction is eas...

Classifying Spaces, Virasoro Equivariant Bundles, Elliptic Cohomology and Moonshine

This work explores some connections between the elliptic cohomology of classifying spaces for finite groups, Virasoro equivariant bundles over their loop spaces and Moonshine for finite groups. Our motivation is as follows: up to homotopy we can replace the loop group LBG by the disjoint union ⨿ [γ]BCG(γ) of classifying spaces of centralizers of elements γ representing conjugacy classes of elem...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

The Sigma Orientation for Analytic Circle-equivariant Elliptic Cohomology

We construct a canonical Thom isomorphism for virtual T-oriented T-equivariant spin bundles with vanishing Borel-equivariant second Chern class, which is natural under pull-back of vector bundles and exponential under Whitney sum. It extends in the rational case the non-equivariant sigma orientation of Hopkins, Strickland, and the author. The construction relates the sigma orientation to the re...