About this Title
Yakov M. Eliashberg, Stanford University, Stanford, CA and William P. Thurston, University of California, Davis, Davis, CA
Publication: University Lecture Series
Publication Year: 1998; Volume 13
ISBNs: 978-0-8218-0776-7 (print); 978-1-4704-2162-5 (online)
MathSciNet review: MR1483314
MSC: Primary 53C15; Secondary 57N10, 57R30, 58F05
This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional “brother” of symplectic geometry.
However, both theories have developed a number of striking similarities. Confoliations—which interpolate between contact structures and codimension-one foliations—should help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other.
A unified approach to the topology of codimension-one foliations and contact geometry.
Insight on the geometric nature of integrability.
New results, in particular on the perturbation of confoliations into contact structures.
Graduate students and research mathematicians working in differential and symplectic geometry, low-dimensional topology, the theory of foliations and several complex variables; some physicists and engineers.
Table of Contents
- Chapter 1. Geometric nature of integrability
- Chapter 2. Perturbation of confoliations into contact structures
- Chapter 3. Taut vs. tight