Group cohomology and equivariant Moore spaces

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...

Co-H-structures on equivariant Moore spaces

Let G be a finite group, OG the category of canonical orbits of G and A : OG → Ab a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A, n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dimX < 2n − 1. If dimX = 2n − 1, then the set of...

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...