Foliations is one of the major concepts of modern geometry and topology meaning a partition of topological space into a disjoint sum of leaves. This book is devoted to geometry and topology of surface foliations and their links to ergodic theory, dynamical systems, complex analysis, differential and noncommutative geometry. It addresses to graduate students and researchers and will serve as a reference book for experts in the field.

A comprehensive, encyclopedic approach to the subject The book is devoted to geometry and topology of surface foliations There are many links to ergodic theory, dynamical systems, complex analysis, differential and noncommutative geometry The book is addressed to graduate students and researchers in the field Includes supplementary material: sn.pub/extras

Inhalt

0. Foliations on 2-Manifolds.- 1. Local Theory.- 2. MorseSmale Foliations.- 3. Foliations Without Holonomy.- 4. Invariants of Foliations.- 5. Curves on Surfaces.- 6. Non-compact Surfaces.- 7. Ergodic Theory.- 8. Homeomorphisms of the Unit Circle.- 9. Diffeomorphisms of Surfaces.- 10. C*-Algebras.- 11. Quadratic Differentials.- 12. Flat Structures.- 13. Principal Curvature Lines.- 14. Differential Equations.- 15. Positive Differential 2Forms.- 16. Control Theory.- 17. Riemann Surfaces.