An equivariant index formula for almost-CR manifolds

Details An equivariant index formula for almost-CR manifolds An equivariant index formula for almost-CR manifolds

2008-10-02

arxiv.org/abs/0810.0338v2

Mathematics

Differential Geometry

17 pages. Version 2 contains a few typo fixes, and updated references

Scientific paper

10.1093/imrn/rnp057

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 in terms of the resulting almost-CR structure that are H-transversally elliptic whenever the action of H is transverse to E. We determine a formula for the H-equivariant index of such symbols that involves only J(E,X) and standard equivariant characteristic classes. This formula generalizes the formula given in arXiv:0712.2431 for the case of a contact manifold.

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