The index of G-transversally elliptic families II

TL;DR

This paper extends the theory of G-transversally elliptic operators by defining their index's Chern character and analyzing the Berline-Vergne formula for families, advancing understanding in equivariant index theory.

Contribution

It introduces a new definition of the Chern character for the index class of G-invariant families of G-transversally elliptic operators and studies related formulas.

Findings

Defined the Chern character of the index class.

Analyzed the Berline-Vergne formula for families.

Extended results to transversally elliptic operators.

Abstract

We define the Chern character of the index class of a $G$-invariant family of $G$-transversally elliptic operators, see [6]. Next we study the Berline-Vergne formula for families in the elliptic and transversally elliptic case.