Equivariant Elliptic Cohomology and Rigidity

Details Equivariant Elliptic Cohomology and Rigidity Equivariant Elliptic Cohomology and Rigidity

1999-12-10

arxiv.org/abs/math/9912089v2

American Journal of Mathematics 123 (2001), 647-677

Mathematics

Algebraic Topology

23 pages

Scientific paper

Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give an invariant definition of S^1-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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