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From Higher Invariants

Title: Perturbative sigma models and elliptic cohomology with complex coefficients

Abstract: I will describe how the geometry of 2|1-dimensional perturbative sigma models can be used to construct elliptic cohomology with complex coefficients and the Witten class of a smooth manifold. Extending the construction to manifolds with the action of a finite group affords an interplay among gauged sigma models, Chern-Simons theory, and twisted equivariant elliptic cohomology. An analogous discussion in dimension 1|1 recovers similar results for twisted equivariant K-theory.