On the connectedness of the space of codimension one foliations on a closed 3-manifold

Abstract

We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late 60's that every plane field can be deformed continuously to an integrable one, so the above inclusion induces a surjective map between connected components. We prove that this map is actually a bijection.

57 pages, 22 figures. This is the last author version before publication, taking into account the referees' reports. Expository changes only, mainly in the appendix

References in corpus (1)

• Connectedness of the space of smooth actions of ${\mathbb{Z}}^n$ on the interval

Cited by in corpus (6)

• Uniqueness of the contact structure approximating a foliation
• On Bott-Morse Foliations and their Poisson Structures in Dimension 3
• Connectedness of the space of smooth actions of ${\mathbb{Z}}^n$ on the interval
• Monopoles and foliations without holonomy-invariant transverse measure
• Novikov's theorem in higher dimensions?
• Foliations, contact structures and their interactions in dimension three