Chern characters in equivariant basic cohomology

Equivariant Cohomological Chern Characters

We construct for an equivariant cohomology theory for proper equivariant CW -complexes an equivariant Chern character, provided that certain conditions about the coefficients are satisfied. These conditions are fulfilled if the coefficients of the equivariant cohomology theory possess a Mackey structure. Such a structure is present in many interesting examples.

Chern-weil Theory and Equivariant Cohomology

An introduction to equivariant cohomology and the equivariant first Chern class

The goal of this paper to provide a relatively accessible and integrated introduction to the algebraic topology of spaces with Lie group actions, in both the smooth and the holomorphic category. We present a detailed treatment of the basic constructions in equivariant de Rham theory and Dolbeault theory. We also discuss equivariant connections and curvature on vector bundles equipped with infin...

Supergeometry in Equivariant Cohomology

We analyze S equivariant cohomology from the supergeometrical point of view. For this purpose we equip the external algebra of given manifold with equivariant even super(pre)symplectic structure, and show, that its Poincare-Cartan invariant defines equivariant Euler classes of surfaces. This allows to derive localization formulae by use of superanalog of Stockes theorem.

Exercises in Equivariant Cohomology

Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory operation connected with the non compactness of the gauge group. The respective roles of fields and observables are emphasized throughout. ENSLAPP-A-619/96 CERN-TH/9...