Differential Borel equivariant cohomology via connections

Abstract

For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the Cartan-Weil equivariant forms and to Borel's equivariant integral cohomology. We show the Chern-Weil homomorphism for equivariant vector bundles with connection naturally factors through differential equivariant cohomology.

40 pages; minor corrections in version 2

References in corpus (2)

• Differential cohomology in a cohesive infinity-topos
• Equivariant Differential Cohomology