Realizing compactly generated pseudo-groups of dimension one

TL;DR

This paper explores how many compactly generated pseudo-groups of one-dimensional local transformations can be realized as the transverse dynamics of codimension-1 foliations on compact 3- or 4-dimensional manifolds.

Contribution

It demonstrates the realizability of a broad class of pseudo-groups as transverse dynamics in low-dimensional foliations.

Findings

Many pseudo-groups are realizable as foliations on 3- or 4-manifolds

Provides conditions under which pseudo-groups can be realized

Advances understanding of the relationship between pseudo-groups and foliations

Abstract

Many compactly generated pseudo-groups of local transformations on 1-manifolds are realizable as the transverse dynamic of a foliation of codimension 1 on a compact manifold of dimension 3 or 4.