Computing the equivariant cohomology of group compactifications

Height Zeta Functions of Equivariant Compactifications of the Heisenberg Group

— We study analytic properties of height zeta functions of equivariant compactifications of the Heisenberg group.

Equivariant Cohomology and Representations of the Symmetric Group

f : Cn(R ) → U(n)/T n from the configuration space of n ordered distinct points of R to the flag manifold of U(n) which is compatible with the natural action of the symmetric group Σn on both spaces. I also noted in [1] that the action of Σn on the rational cohomology of either space coincides with the regular representation but that the homomorphism f induced by f cannot possibly be an isomorp...

Intersection cohomology of B ×B-orbit closures in group compactifications

An adjoint semi-simple group G has a “wonderful” compactification X, which is a smooth projective variety, containing G as an open subvariety. X is acted upon by G×G and, B denoting a Borel subgroup of G, the group B × B has finitely many orbits in X. The main results of this paper concern the intersection cohomology of the closures of the B × B-orbits. Examples of such closures are the “large ...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

Applications of Equivariant Cohomology

We will discuss the equivariant cohomology of a manifold endowed with the action of a Lie group. Localization formulae for equivariant integrals are explained by a vanishing theorem for equivariant cohomology with generalized coefficients. We then give applications to integration of characteristic classes on symplectic quotients and to indices of transversally elliptic operators. In particular,...