Induction functor in noncommutative equivariant cohomology and Dirac cohomology

Induction Functor in Non-commutative Equivariant Cohomology and Dirac Cohomology

The aim of this paper is to put some recent results of HuangPandz̆ić (conjectured by Vogan) and Kostant on Dirac cohomology in a broader perspective. This is achieved by introducing an induction functor in the noncommutative equivariant cohomology. In this context, the results of Huang-Pandz̆ić and Kostant are interpreted as special cases (corresponding to the manifold being a point) of more gene...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Equivariant Cohomology and Resolution

The ‘Folk Theorem’ that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a ‘resolution tower’ which projects to a resolution, with iterated boundary fibration, of the quotient. Equivaria...

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...