Equivariant Differential Cohomology

2015/10/21 by Kübel, Andreas, Thom, Andreas
#Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.06392

Abstract

The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action on the manifold: The definition of equivariant characteristic forms in the Cartan model due to Nicole Berline and Michèle Vergne motivates a refinement of equivariant integral cohomology by all Cartan cocycles. In view of this, we will also review previous definitions critically, in particular the one given by Kiyonori Gomi.

Related

• Equivariant characteristic forms in the Cartan model and Borel equivariant cohomology
• Equivariant de Rham Cohomology: Theory and Applications
• Differential Borel equivariant cohomology via connections
• Equivariant characteristic classes in the Cartan model
• Differential Cohomology: Categories, Characteristic Classes, and Connections