A construction of complex analytic elliptic cohomology from double free loop spaces
Abstract
We construct a complex analytic version of an equivariant cohomology theory which appeared in a recent paper of Rezk, and which is roughly modeled on the Borelequivariant cohomology of the double free loop space. The construction is defined on finite, torusequivariant CW complexes and takes values in coherent holomorphic sheaves over the moduli stack of complex elliptic curves. Our methods involve an inverse limit construction over all finite dimensional subcomplexes of the double free loop space, following an analogous construction of Kitchloo for single free loop spaces. We show that, for any given complex elliptic curve $\mathcal{C}$, the fiber of our construction over $\mathcal{C}$ is isomorphic to Grojnowski's equivariant elliptic cohomology theory associated to $\mathcal{C}$.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.05659
 Bibcode:
 2019arXiv191005659S
 Keywords:

 Mathematics  Algebraic Topology