An equivariant index formula in contact geometry

An equivariant index formula in contact geometry

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalized coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...

An equivariant index formula for elliptic actions on contact manifolds

Given an elliptic action of a compact Lie group G on a co-oriented contact manifold (M, E) one obtains two naturally associated objects: A G-transversally elliptic operator Db / , and an equivariant differential form with generalised coefficients J (E, X) defined in terms of a choice of contact form on M . We explain how the form J (E, X) is natural with respect to the contact structure, and gi...

An equivariant index formula for almost-CR manifolds

We consider a consider the case of a compact manifold M , together with the following data: the action of a compact Lie group H and a smooth H-invariant distribution E, such that the H-orbits are transverse to E. These data determine a natural equivariant differential form with generalized coefficients J (E,X) whose properties we describe. When E is equipped with a complex structure, we define ...

Equivariant Algebraic Geometry

Equivariant Cohomology in Algebraic Geometry Lecture Fifteen: Chevalley’s Formula, Line Bundles, Duality

In the equivariant setting, Chevalley’s formula computes the product of a divisor class y(sα), for α a simple root, and a general class y(v), for v ∈ W . This will involve classes y(w), for w = v, and for v ≤ w with l(w) = l(v)+1. In the latter case, such w can be written uniquely in the form w = v sβ, for some positive root β, with γ = v−1(β) also positive, and w = sγ v. (It is a general fact ...