Ebook: Foliations on Surfaces
Author: Igor Nikolaev (auth.)
- Tags: Manifolds and Cell Complexes (incl. Diff.Topology), Global Analysis and Analysis on Manifolds, Combinatorics
- Series: Ergebnisse der Mathematik und ihrer Grenzgebiete 41
- Year: 2001
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
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
Content:
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
....
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