## Advanced Studies in Pure Mathematics

### Cones of foliations almost without holonomy

#### Abstract

On sutured 3-manifolds $M$, we classify taut foliations almost without holonomy up to isotopy. We assume that the compact leaves lie in $\partial M$. The classification is given by finitely many convex, polyhedral cones in $H^{1}(M;\mathbb{R})$ which have disjoint interiors. The classes in the interiors of these cones determine the isotopy classes. This work relies heavily on the Handel–Miller classification of the isotopy classes of endperiodic surface automorphisms. While the Handel–Miller theory was not published by the originators, the authors have given a complete account elsewhere.

#### Article information

Dates
Revised: 7 August 2015
First available in Project Euclid: 4 October 2018

https://projecteuclid.org/ euclid.aspm/1538671774

Digital Object Identifier
doi:10.2969/aspm/07210301

Mathematical Reviews number (MathSciNet)
MR3726717

Zentralblatt MATH identifier
1388.57023

Subjects
Primary: 57R30: Foliations; geometric theory

#### Citation

Cantwell, John; Conlon, Lawrence. Cones of foliations almost without holonomy. Geometry, Dynamics, and Foliations 2013: In honor of Steven Hurder and Takashi Tsuboi on the occasion of their 60th birthdays, 301--348, Mathematical Society of Japan, Tokyo, Japan, 2017. doi:10.2969/aspm/07210301. https://projecteuclid.org/euclid.aspm/1538671774