Quasicomplementary foliations and the Mather–Thurston theorem

Abstract

We establish a form of the h–principle for the existence of foliations of codimension at least $2$ which are quasicomplementary to a given one. Roughly, “quasicomplementary” means that they are complementary except on the boundaries of some kind of Reeb components. The construction involves an adaptation of W Thurston’s “inflation” process. The same methods also provide a proof of the classical Mather–Thurston theorem.