Pansu pullback and spectral complexes

TL;DR

This paper establishes the compatibility of Pansu pullback with spectral complex differentials in Carnot groups and introduces a method to lift Pansu derivatives to central extensions, advancing geometric analysis in sub-Riemannian geometry.

Contribution

It proves the commutativity of Pansu pullback with spectral differentials and provides a novel approach to lift Pansu derivatives to central extensions of Carnot groups.

Findings

Proved the commutativity between Pansu pullback and spectral differentials.

Developed a method to lift Pansu derivatives to central extensions.

Enhanced understanding of geometric structures in Carnot groups.

Abstract

In this paper, we prove the commutativity between the Pansu pullback of a smooth contact map between Carnot groups and the differentials appearing in the spectral complexes. As a direct application, we also present a way of "lifting" a Pansu derivative (viewed as a Lie algebra homomorphism) from Carnot groups to their central extensions.