The $h$-principle for maps transverse to bracket-generating distributions

Aritra Bhowmick

Vol. 330 (2024), No. 2, 207–231

DOI: 10.2140/pjm.2024.330.207

Abstract

Given a smooth bracket-generating distribution $\mathcal{𝒟}$ of constant growth on a manifold $M$, we prove that maps from an arbitrary manifold $\mathrm{\Sigma }$ to $M$, which are transverse to $\mathcal{𝒟}$, satisfy the complete $h$-principle. This partially settles a question posed by M. Gromov (1986).

Keywords

transverse maps, bracket-generating distributions, $h$-principle

Mathematical Subject Classification

Primary: 58A20, 58A30

Secondary: 57R42, 58A17

Milestones

Received: 24 May 2022

Revised: 24 July 2023

Accepted: 8 June 2024

Published: 13 September 2024