Equivariant covering spaces and cohomology

Arc Spaces and Equivariant Cohomology

We present a new geometric interpretation of equivariant cohomology in which one replaces a smooth, complex G-variety X by its associated arc space J∞X, with its induced G-action. This not only allows us to obtain geometric classes in equivariant cohomology of arbitrarily high degree, but also provides more flexibility for equivariantly deforming classes and geometrically interpreting multiplic...

Equivariant Quantum Cohomology of Homogeneous Spaces

We prove a Chevalley formula for the equivariant quantum multiplication of two Schubert classes in the homogeneous variety X = G/P . As in the case when X is a Grassmannian ([Mi1]), this formula implies an algorithm to compute the structure constants of the equivariant quantum cohomology algebra of X.

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant 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...

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...