Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomology

Equivariant Singular Homology and Cohomology

Let G be a topological group. By a G-space X we mean a topological space X together with a left action of G on X. Under the assumption that G is a compact Lie group, a discrete group or an abelian locally compact group, we constructed in [5] (see also [6]) an equivariant homology and cohomology theory, defined on the category of all G-pairs and G-maps, which both satisfy all seven equivariant E...

Equivariant cohomology and equivariant intersection theory

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures given at Montréal is Summer 1997. Our main aim is to obtain explicit descriptions of cohomology or Chow rings of certain manifolds with group actions which ar...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Giambelli Formulae for the Equivariant Quantum Cohomology of the Grassmannian

We find presentations by generators and relations for the equivariant quantum cohomology of the Grassmannian. For these presentations, we also find determinantal formulae for the equivariant quantum Schubert classes. To prove this, we use the theory of factorial Schur functions and a characterization of the equivariant quantum cohomology ring.

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...