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.

Readership

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.