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Foliations II
Alberto Candel, California State University, Northridge, CA, and Lawrence Conlon, Washington University, St. Louis, MO
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2003; 545 pp; hardcover
Volume: 60
ISBN-10: 0-8218-0881-8
ISBN-13: 978-0-8218-0881-8
List Price: US$87 Member Price: US$69.60
Order Code: GSM/60

Foliations I - Alberto Candel and Lawrence Conlon

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 highly-developed area of mathematics. In all cases, the authors present useful, in-depth 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.

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 first-rate ... diagrams ... are well-crafted 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 well-chosen 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."

"The large number of well-chosen 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

Part 1: Analysis and geometry on foliated spaces
• Foreword to part 1
• The $$C^*$$-algebra of a foliated space
• Harmonic measures for foliated spaces
• Generic leaves
Part 2: Characteristic classes and foliations
• Foreword to part 2
• The Euler class of circle bundles
• The Chern-Weil construction
• Characteristic classes and integrability
• The Godbillon-Vey classes
Part 3: Foliated 3-manifolds
• Foreword to part 3
• Constructing foliations
• Reebless foliations
• Foliations and the Thurston norm
• Disk decomposition and foliations of link complements
• $$C^*$$-Algebras
• Riemannian geometry and heat diffusion
• Brownian motion
• Planar foliations
• Bibliography
• Index