On the deformation groupoid of the inhomogeneous pseudo-differential Calculus

TL;DR

This paper constructs a deformation groupoid framework for inhomogeneous pseudo-differential calculus, generalizing previous models and providing an elementary construction method for these mathematical structures.

Contribution

It offers a new, elementary construction of the deformation groupoid for inhomogeneous pseudo-differential calculus and extends it to filtrations of the tangent bundle.

Findings

Unified construction of the deformation groupoid for inhomogeneous calculus

Extension to filtrations of the tangent bundle

Simplification of the understanding of the calculus structure

Abstract

In 1974, Folland and Stein constructed an inhomogeneous pseudo-differential calculus based on analysis on the Heisenberg group. This Heisenberg calculus was generalized by several authors, to any subbundle of the tangent bundle. van Erp and Yuncken, following Debord and Skandalis showed that this calculus can be recovered using a deformation groupoid alla tangent groupoid of Connes. Using functoriality of the deformation to the normal cone construction, we give an elementary construction of this groupoid. We then extend it to the general case of a filtration of the tangent bundle by an iterated deformation.