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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.
List of contents
0. Foliations on 2-Manifolds.- 1. Local Theory.- 2. Morse-Smale 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 2-Forms.- 16. Control Theory.- 17. Riemann Surfaces.
Summary
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.
