1 - Introduction

Summary

This book is about the geometry and topology of symplectic manifolds equipped with pairs of complementary Lagrangian foliations. The resulting structure is very rich, intertwining symplectic geometry, the theory of foliations, dynamical systems, and pseudo-Riemannian geometry in interesting ways.

Before describing the contents of the book in detail, we want to discuss a few motivating vignettes. The first two of these are to be kept in mind as motivational background, whereas the third and fourth ones will be taken up again and again later in the book.