Equivariant Bundles and Cohomology

Classifying Spaces, Virasoro Equivariant Bundles, Elliptic Cohomology and Moonshine

This work explores some connections between the elliptic cohomology of classifying spaces for finite groups, Virasoro equivariant bundles over their loop spaces and Moonshine for finite groups. Our motivation is as follows: up to homotopy we can replace the loop group LBG by the disjoint union ⨿ [γ]BCG(γ) of classifying spaces of centralizers of elements γ representing conjugacy classes of elem...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

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...

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...

Equivariant Bundles and Isotropy Representations

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...