Equivariant differential cohomology
Copyright policy )Equivariant differential cohomology
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 Mich��le 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.
47 pages
- TU Dresden Germany
Mathematics - Differential Geometry, Cartan model, Borel cohomology, differential forms, differential characteristic classes, Chern class, Differential Geometry (math.DG), Characteristic classes and numbers in differential topology, Homology of classifying spaces and characteristic classes in algebraic topology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Generalized (extraordinary) homology and cohomology theories in algebraic topology, vector bundle, de Rham theory in global analysis
Mathematics - Differential Geometry, Cartan model, Borel cohomology, differential forms, differential characteristic classes, Chern class, Differential Geometry (math.DG), Characteristic classes and numbers in differential topology, Homology of classifying spaces and characteristic classes in algebraic topology, FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Generalized (extraordinary) homology and cohomology theories in algebraic topology, vector bundle, de Rham theory in global analysis
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