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.