Equivariant elliptic cohomology and the 2-loop groupoid

Abstract

Following an outline of Rezk, we give a construction of complex-analytic $G$-equivariant elliptic cohomology for an arbitrary compact Lie group $G$ and we prove some of its fundamental properties. The construction is parametrised over the orbit category of the groupoid of principal $G$-bundles over 2-dimensional tori and generalises Grojnowski's construction of equivariant elliptic cohomology.

38 pages. Submitted version. Exposition improved, citations and references added, Section 6.6 added. Theorem C removed due to an error (to be fixed and included in a subsequent paper)