SIGMA 22 (2026), 078, 8 pages      arXiv:2507.13049      https://doi.org/10.3842/SIGMA.2026.078

A Note on Pliability and the Openness of the Multiexponential Map in Carnot Groups

Frédéric Jean ^a, Mario Sigalotti ^b and Alessandro Socionovo ^a
a) Unité de Mathématiques Appliquées, ENSTA, Institut Polytechnique de Paris, 91120 Palaiseau, France
^b) Laboratoire Jacques-Louis Lions, Sorbonne Université, Université de Paris, CNRS, Inria, Paris, France

Received March 06, 2026, in final form August 11, 2026; Published online August 19, 2026

Abstract
In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions.

Key words: pliability; rigidity; multiexponential map; Carnot group; endpoint map.

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