Index of transversally elliptic operators

TL;DR

This paper introduces a novel approach to computing the index of transversally elliptic operators using equivariant Chern characters with generalized coefficients and compact support, building on previous work by the authors.

Contribution

It presents a new perspective on cohomological formulas for the index, utilizing advanced equivariant Chern characters with generalized coefficients.

Findings

New cohomological formula for transversally elliptic operators

Use of equivariant Chern characters with generalized coefficients

Extension of previous work on equivariant cohomology

Abstract

In 1996, Berline and Vergne gave a cohomological formula for the index of a transversally elliptic operator. In this paper we propose a new point of view where the cohomological formulae make use of equivariant Chern characters with generalized coefficients and with compact suppport. This kind of Chern characters was studied by the authors in a previous paper (see arXiv:0801.2822).