A construction of complex analytic elliptic cohomology from double free loop spaces. (26th August 2021) - Spong, Matthew
Abstract : We construct a complex analytic version of an equivariant cohomology theory which appeared in a paper of Rezk, and which is roughly modelled on the Borel-equivariant cohomology of the double free loop space. The construction is defined on finite, torus-equivariant 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 C, the fiber of our construction over C is isomorphic to Grojnowski's equivariant elliptic cohomology theory associated to C .