Applications of Equivariant Cohomology

Details Applications of Equivariant Cohomology Applications of Equivariant Cohomology

2006-07-17

arxiv.org/abs/math/0607389v2

Mathematics

Differential Geometry

This text is to be submitted to the Proceedings of the International Congress of Mathematicians, Madrid, August 2006. Minor ch

Scientific paper

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.

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