Open Saturated Sets Without Holonomy

Abstract

Open, connected, saturated sets W without holonomy in codimension one foliations play key roles as fundamental building blocks. Here, for the case of foliated 3-manifolds, we produce a finite system of closed, convex, non-overlapping polyhedral cones in the first cohomology of W with real coefficients such that the isotopy classes of possible foliations of W without holonomy, either dense leaved in W or proper, correspond one-to-one to the rays in the interiors of these cones. This generalizes our classification of depth one foliations to foliations of finite depth and more general foliations.

This version is an extension and substantial revision of the previous version

Cited by in corpus (2)

• Endperiodic Automorphisms of Surfaces and Foliations
• The sutured Floer polytope and taut depth one foliations