Equivariant Elliptic Cohomology and Rigidity
Ioanid Rosu
Abstract
Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give an invariant definition of S1-equivariant elliptic cohomology, and use it to give an entirely cohomological proof of the rigidity theorem of Witten for the elliptic genus. We also state and prove a rigidity theorem for families of elliptic genera.
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