Topology of foliations : an introduction
著者
書誌事項
Topology of foliations : an introduction
(Translations of mathematical monographs, v. 97)
American Mathematical Society, c1992
- : softcover
- タイトル別名
-
Yousou no toporojii
Yōsō no toporojī
葉層のトポロジー
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注記
Translation of: 葉層のトポロジー
Includes bibliographical references and index
内容説明・目次
- 巻冊次
-
: softcover ISBN 9780821842003
内容説明
This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.
目次
- Nonsingular dynamical systems on the torus
- $Cr$ manifolds and tangent spaces
- Dynamical systems and limit sets
- Foliations
- Stability theorems on foliations
- The existence of compact leaves
- Foliations and differential forms
- Cobordisms of foliations
- Appendices
- Translator's afterword
- Subject index
- Nonsingular dynamical systems on the torus
- $Cr$ manifolds and tangent spaces
- Dynamical systems and limit sets
- Foliations
- Stability theorems on foliations
- The existence of compact leaves
- Foliations and differential forms
- Cobordisms of foliations
- Appendices
- Translator's afterword
- Subject index
- 巻冊次
-
ISBN 9780821845431
内容説明
This book provides historical background and a complete overview of the qualitative theory of foliations and differential dynamical systems. Senior mathematics majors and graduate students with background in multivariate calculus, algebraic and differential topology, differential geometry, and linear algebra will find this book an accessible introduction. Upon finishing the book, readers will be prepared to take up research in this area. Readers will appreciate the book for its highly visual presentation of examples in low dimensions. The author focuses particularly on foliations with compact leaves, covering all the important basic results. Specific topics covered include: dynamical systems on the torus and the three-sphere, local and global stability theorems for foliations, the existence of compact leaves on three-spheres, and foliated cobordisms on three-spheres. Also included is a short introduction to the theory of differentiable manifolds.
目次
Nonsingular dynamical systems on the torus $C^r$ manifolds and tangent spaces Dynamical systems and limit sets Foliations Stability theorems on foliations The existence of compact leaves Foliations and differential forms Cobordisms of foliations.
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