Thurston's h-principle for 2-dimensional Foliations of Codimension Greater than One

TL;DR

This paper revisits Thurston's unpublished proof demonstrating that any smooth 2-plane field on a manifold of dimension at least 4 can be homotoped to a foliation, confirming the h-principle in this context.

Contribution

The paper provides a detailed recreation of Thurston's original proof establishing the h-principle for 2-dimensional foliations in higher-dimensional manifolds.

Findings

Any smooth 2-plane field on a manifold of dimension ≥4 is homotopic to a foliation.

The proof confirms the h-principle for 2-dimensional foliations in higher dimensions.

Thurston's original unpublished proof is reconstructed and validated.

Abstract

We recreate an unpublished proof of William Thurston from the early 1970's that any smooth 2-plane field on a manifold of dimension at least 4 is homotopic to the tangent plane field of a foliation.