On the deformation groupoid of the inhomogeneous pseudo-differential Calculus
Differential Geometry
2021-12-07 v3
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.
Keywords
Cite
@article{arxiv.1806.08585,
title = {On the deformation groupoid of the inhomogeneous pseudo-differential Calculus},
author = {Omar Mohsen},
journal= {arXiv preprint arXiv:1806.08585},
year = {2021}
}
Comments
Made changes suggested by the referee