New York Journal of Mathematics
Volume 23 (2017) 441-487


Corbett Redden

Differential Borel equivariant cohomology via connections

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Published: March 28, 2017
Keywords: Differential cohomology, equivariant cohomology, Chern-Weil
Subject: 53C08, 55N91, 53C05

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.


The author thanks the Hausdorff Institute for Mathematics for its support and hospitality during his visit.

Author information

Department of Mathematics, LIU Post, Long Island University, 720 Northern Blvd, Brookville, NY 11548, USA