Applications of Equivariant Cohomology

Abstract

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, we state a conjecture for the index of a transversally elliptic operator linked to a Hamiltonian action. In the last part, we describe algorithms for numerical computations of values of multivariate spline functions and of vector-partition functions of classical root systems.

This text is to be submitted to the Proceedings of the International Congress of Mathematicians, Madrid, August 2006. Minor changes and added references

References in corpus (2)

• The volume of the 10th Birkhoff polytope
• Witten's Nonabelian Localization for Noncompact Hamiltonian Spaces

Cited by in corpus (8)

• A fixed point formula for the index of multi-centered N=2 black holes
• Index of transversally elliptic operators
• Equivariant relative Thom forms and Chern characters
• Equivariant Chern characters with generalized coefficients
• An equivariant index formula for elliptic actions on contact manifolds
• A K-homological approach to the quantization commutes with reduction problem
• Formal geometric quantization II
• Background cohomology of a non-compact Kahler G-manifold