Foliations on Surfaces (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 41)

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. Front Matter....Pages I-XXVI Foliations on 2-Manifolds....Pages 1-18 Front Matter....Pages 19-19 Local Theory....Pages 21-35 Morse-Smale Foliations....Pages 37-65 Foliations Without Holonomy....Pages 67-123 Invariants of Foliations....Pages 125-190 Curves on Surfaces....Pages 191-222 Non-compact Surfaces....Pages 223-237 Front Matter....Pages 239-239 Ergodic Theory....Pages 241-259 Homeomorphisms of the Unit Circle....Pages 261-293 Diffeomorphisms of Surfaces....Pages 295-303 C*-Algebras....Pages 305-330 Quadratic Differentials....Pages 331-340 Flat Structures....Pages 341-351 Principal Curvature Lines....Pages 353-373 Differential Equations....Pages 375-382 Positive Differential 2-Forms....Pages 383-390 Control Theory....Pages 391-398 Front Matter....Pages 399-399 Riemann Surfaces....Pages 401-429 Back Matter....Pages 431-450 Foliations on 2-Manifolds General Theory Local Theory. Morse-Smale Foliations. Foliations Without Holonomy. Invariants of Foliations. Curves on Surfaces. Non-compact Surfaces Applications Ergodic Theory. Homeomorphisms of the Unit Circle. Diffeomorphisms of Surfaces. C*-Algebras. Quadratic Differentials. Flat Structures. Principal Curvature Lines. Differential Equations. Positive Differential 2-forms. Control Theory (by B. Piccoli) Appendix Riemann Surfaces. "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 book addresses graduate students and researchers and will serve as a reference book for experts in the field."--Jacket

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.