Index theorem for inhomogeneous hypoelliptic differential operators

TL;DR

This paper establishes an index theorem for inhomogeneous hypoelliptic differential operators satisfying the Rockland condition, extending previous results for contact manifolds to a broader class of operators.

Contribution

It generalizes the index theorem for contact manifolds to include inhomogeneous hypoelliptic operators satisfying the Rockland condition.

Findings

Proved an index theorem for a new class of hypoelliptic operators.

Extended Van-Erp's index theorem to inhomogeneous operators.

Demonstrated the applicability of the theorem to broader geometric contexts.

Abstract

We prove an index theorem for inhomogeneous differential operators satisfying the Rockland condition (hence hypoelliptic). This theorem extends an index theorem for contact manifolds by Van-Erp.