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Equivariant elliptic cohomology and rigidity
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 123, Number 4, August 2001
- pp. 647-677
- 10.1353/ajm.2001.0027
- Article
- Additional Information
Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give an invariant definition of complex 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.