Quasi-Complementary Foliations and the Mather-Thurston Theorem

TL;DR

This paper proves a version of the h-principle for foliations that are quasi-complementary to a given foliation and offers a new proof of the classical Mather-Thurston theorem using these methods.

Contribution

It introduces a new h-principle for quasi-complementary foliations and provides an alternative proof of the Mather-Thurston theorem.

Findings

Established a form of the h-principle for quasi-complementary foliations

Provided a new proof of the Mather-Thurston theorem

Extended the understanding of foliation existence conditions

Abstract

We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.