Index of projective elliptic operators

TL;DR

This paper computes the equivariant index of transversally elliptic operators derived from projective elliptic operators on manifolds with Azumaya bundles, extending the fractional index formula.

Contribution

It provides a new computation of the equivariant index for a class of transversally elliptic operators related to projective elliptic operators, generalizing existing fractional index formulas.

Findings

Derived explicit equivariant index formulas

Extended fractional index formula to new operator classes

Connected projective elliptic operators with transversally elliptic operators

Abstract

Mathai, Melrose, and Singer introduced the notion of projective elliptic operators on manifolds equipped with an Azumaya bundle. In this note we compute the equivariant index of transversally elliptic operators that are the pullback of projective elliptic operators on the trivialization of the Azumaya bundle. It encompasses the fractional index formula of projective elliptic operator by Mathai-Melrose-Singer.