Title: Equivariant Elliptic Cohomology and Rigidity
Author: Ioanid Rosu,
AMS Classification numbers: 55N34; 55N91
xxx LANL archive ID number: AT/9912089
Addresses and emails of Authors:
Ioanid Rosu, M.I.T., Cambridge, MA.
ioanid@math.mit.edu
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.