An equivalence relation for codimension one foliations of 3-manifolds

Sandra Shields

Vol. 175 (1996), No. 1, 235–256

DOI: 10.2140/pjm.1996.175.235

Abstract

We consider codimension one foliations of closed, Reimannian 3-manifolds. We show all branched surfaces constructed from a foliation and a transverse flow are conjugate. We use branched surfaces to define an equivalence relation on foliations transverse to the same nonsingular flow. Under this relation, foliations in the same equivalence class need not be topologically conjugate yet they will share important qualitative properties.

Mathematical Subject Classification 2000

Primary: 57R30

Secondary: 57N10

Milestones

Received: 10 May 1994

Published: 1 September 1996