Foliations on Surfaces [Paperback]

This book presents a comprehensive, encyclopedic approach to the subject of foliations, one of the major concepts of modern geometry and topology. It addresses graduate students and researchers and serves as a reference book for experts in the field.

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. This comprehensive book addresses graduate students and researchers and will serve as a reference book for experts in the field.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.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 fieldSpringer Book Archives