An equivariant index formula for elliptic actions on contact manifolds

Details An equivariant index formula for elliptic actions on contact manifolds An equivariant index formula for elliptic actions on contact manifolds

2007-12-14

arxiv.org/abs/0712.2431v4

Mathematics

Differential Geometry

23 pages; Final (publication) version - to appear in MRL. Further typo fixes, extension of final corollary from formula at the

Scientific paper

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 $\dirac$, and an equivariant differential form with generalised coefficients $\mathcal{J}(E,X)$ defined in terms of a choice of contact form on $M$. We explain how the form $\mathcal{J}(E,X)$ is natural with respect to the contact structure, and give a formula for the equivariant index of $\dirac$ involving $\mathcal{J}(E,X)$. A key tool is the Chern character with compact support developed by Paradan-Vergne \cite{PV1,PV}.

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