The $h$-Principle for Maps Transverse to Bracket-Generating Distributions

Abstract

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

Added constant growth hypothesis to the main result. Added 2 figures. To appear in Pacific J. of Math