EQUIVARIANT COHOMOLOGY OF RATIONALLY SMOOTH GROUP EMBEDDINGS

Equivariant Embeddings into Smooth Toric Varieties

We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well-known embedding theorem of Sumihiro on quasiprojective G-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extend...

Geometric Quantization and Equivariant Cohomology Geometric Quantization and Equivariant Cohomology

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...

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,...

Equivariant Formal Group Laws and Complex Oriented Cohomology Theories

The article gives an introduction to equivariant formal group laws, and explains its relevance to complex oriented cohomol-ogy theories in general and to complex cobordism in particular.