Regularization of Gamma_1-structures in dimension 3

TL;DR

This paper presents a simplified proof of Thurston's regularization theorem for Gamma_1-structures on 3-manifolds, with specific foliation types in co-orientable cases, avoiding complex prior methods.

Contribution

It offers a straightforward proof of Thurston's regularization theorem and characterizes the resulting foliations in co-orientable cases, including a model for non co-orientable cases.

Findings

Simplified proof of Thurston's regularization theorem

Foliations can be chosen as open book foliations modified by suspension

Models provided for non co-orientable cases

Abstract

For $\Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in \cite{thurston}, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting foliation can be chosen of a precise kind, namely an "open book foliation modified by suspension." There is also a model in the non co-orientable case.