An equivariant index formula for almost-CR manifolds
نویسنده
چکیده
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 a class of symbol mappings σ in terms of the resulting almost-CR structure that are H-transversally elliptic whenever the action ofH is transverse to E. We determine a formula for theH-equivariant index of such symbols that involves only J (E,X) and standard equivariant characteristic classes. This formula generalizes the formula given in [9] for the case of a contact manifold.
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