An equivariant index formula for elliptic actions on contact manifolds

Abstract

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}.

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

References in corpus (2)

• Equivariant relative Thom forms and Chern characters
• Equivariant Chern characters with generalized coefficients