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Hardcover ISBN:  9780821808818 
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Book DetailsGraduate Studies in MathematicsVolume: 60; 2003; 545 ppMSC: Primary 57
This is the second of two volumes on the qualitative theory of foliations. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds. Each of these is an example of deep interaction between foliation theory and some other highlydeveloped area of mathematics. In all cases, the authors present useful, indepth introductions, which lead to further study using the extensive available literature.
This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. It contains exercises and many illustrations. The book would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations I is Volume 23 in the AMS series, Graduate Studies in Mathematics.
ReadershipGraduate students and research mathematicians interested in foliated spaces.

Table of Contents

Part 1: Analysis and geometry on foliated spaces

Foreword to part 1

Chapter 1. The $C^*$algebra of a foliated space

Chapter 2. Harmonic measures for foliated spaces

Chapter 3. Generic leaves

Part 2: Characteristic classes and foliations

Foreword to part 2

Chapter 4. The Euler class of circle bundles

Chapter 5. The ChernWeil construction

Chapter 6. Characteristic classes and integrability

Chapter 7. The GodbillonVey classes

Part 3: Foliated 3manifolds

Foreword to part 3

Chapter 8. Constructing foliations

Chapter 9. Reebless foliations

Chapter 10. Foliations and the Thurston norm

Chapter 11. Disk decomposition and foliations of link complements

Appendices

Appendix A. $C^*$Algebras

Appendix B. Riemannian geometry and heat diffusion

Appendix C. Brownian motion

Appendix D. Planar foliations


Additional Material

Reviews

Both volumes are written with great care and a deep knowledge of the subject ... provide the most extensive elaboration of several aspects of foliation theory.
Mathematical Reviews 
From reviews for Foliations I:
Overall presentation is firstrate ... diagrams ... are wellcrafted and reflect the strongly ‘graphical’ nature of the subject ... A prospective reader who cares to invest the time needed to plough seriously through the book ought to be rewarded with a gratifying mathematical experience ... can also be recommended to more advanced researchers, who would enjoy seeing a compendium of major results.
Bulletin of the LMS 
The authors pay great attention to examples, and you can find a large number of them in the book ... They are wellchosen and will keep the interest of the reader on a high level ... [The book is] a fundamental source for everybody with a serious interest in foliations.
European Mathematical Society Newsletter 
The large number of wellchosen examples is one of the most striking features of the book ... [It] contains several beautiful figures which help one to imagine and better understand situations described formally in the text. Therefore, graduate students, young researchers, and in fact, everybody interested in foliations should profit from this book.
Mathematical Reviews


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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This is the second of two volumes on the qualitative theory of foliations. For this volume, the authors have selected three special topics: analysis on foliated spaces, characteristic classes of foliations, and foliated manifolds. Each of these is an example of deep interaction between foliation theory and some other highlydeveloped area of mathematics. In all cases, the authors present useful, indepth introductions, which lead to further study using the extensive available literature.
This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. It contains exercises and many illustrations. The book would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations I is Volume 23 in the AMS series, Graduate Studies in Mathematics.
Graduate students and research mathematicians interested in foliated spaces.

Part 1: Analysis and geometry on foliated spaces

Foreword to part 1

Chapter 1. The $C^*$algebra of a foliated space

Chapter 2. Harmonic measures for foliated spaces

Chapter 3. Generic leaves

Part 2: Characteristic classes and foliations

Foreword to part 2

Chapter 4. The Euler class of circle bundles

Chapter 5. The ChernWeil construction

Chapter 6. Characteristic classes and integrability

Chapter 7. The GodbillonVey classes

Part 3: Foliated 3manifolds

Foreword to part 3

Chapter 8. Constructing foliations

Chapter 9. Reebless foliations

Chapter 10. Foliations and the Thurston norm

Chapter 11. Disk decomposition and foliations of link complements

Appendices

Appendix A. $C^*$Algebras

Appendix B. Riemannian geometry and heat diffusion

Appendix C. Brownian motion

Appendix D. Planar foliations

Both volumes are written with great care and a deep knowledge of the subject ... provide the most extensive elaboration of several aspects of foliation theory.
Mathematical Reviews 
From reviews for Foliations I:
Overall presentation is firstrate ... diagrams ... are wellcrafted and reflect the strongly ‘graphical’ nature of the subject ... A prospective reader who cares to invest the time needed to plough seriously through the book ought to be rewarded with a gratifying mathematical experience ... can also be recommended to more advanced researchers, who would enjoy seeing a compendium of major results.
Bulletin of the LMS 
The authors pay great attention to examples, and you can find a large number of them in the book ... They are wellchosen and will keep the interest of the reader on a high level ... [The book is] a fundamental source for everybody with a serious interest in foliations.
European Mathematical Society Newsletter 
The large number of wellchosen examples is one of the most striking features of the book ... [It] contains several beautiful figures which help one to imagine and better understand situations described formally in the text. Therefore, graduate students, young researchers, and in fact, everybody interested in foliations should profit from this book.
Mathematical Reviews