Confoliations - v. 13

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.

Features: 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.