# An equivariant index formula for elliptic actions on contact manifolds - Mathematics > Differential Geometry

Abstract: Given an elliptic action of a compact Lie group $G$ on a co-oriented contactmanifold $M,E$ one obtains two naturally associated objects: A$G$-transversally elliptic operator $\dirac$, and an equivariant differentialform with generalised coefficients $\mathcal{J}E,X$ defined in terms of achoice of contact form on $M$. We explain how the form $\mathcal{J}E,X$ isnatural with respect to the contact structure, and give a formula for theequivariant index of $\dirac$ involving $\mathcal{J}E,X$. A key tool is theChern character with compact support developed by Paradan-Vergne \cite{PV1,PV}.

Author: Sean Fitzpatrick

Source: https://arxiv.org/