Cyclic cohomology and the extended Heisenberg calculus of Epstein and Melrose

TL;DR

This paper derives an index formula for pseudodifferential operators within the extended Heisenberg calculus, expanding previous work on the Heisenberg calculus by including broader classes of operators.

Contribution

It introduces a new index formula applicable to the extended Heisenberg calculus, generalizing earlier results focused on the standard Heisenberg calculus.

Findings

Derived an explicit index formula for the extended Heisenberg calculus.

Extended previous results from the Heisenberg calculus to a broader class of operators.

Provided theoretical foundations for future applications in analysis and geometry.

Abstract

In this paper we present a formula for the index of a pseudodifferential operator with invertible principal symbol in the extended Heisenberg calculus of Epstein and Melrose. Our results build on the work we did in a previous paper (arXiv:2010.02900), where we restricted attention to the Heisenberg calculus proper.