Foliations I (Graduate Studies in Mathematics) by Alberto Candel and Lawrence Conlon (PDF)

Description

This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a “primer” in foliation theory. A working knowledge of manifold theory and topology is a prerequisite. Fundamental definitions and theorems are explained to prepare the reader for further exploration of the topic. This section places considerable emphasis on the construction of examples, which are accompanied by many illustrations. Part 2 considers foliations of codimension one. Using very hands-on geometric methods, the path leads to a complete structure theory (the theory of levels), which was established by Conlon along with Cantwell, Hector, Duminy, Nishimori, Tsuchiya, et al. Presented here is the first and only full treatment of the theory of levels in a textbook. Part 3 is devoted to foliations of higher codimension, including abstract laminations (foliated spaces). The treatment emphasizes the methods of ergodic theory: holonomy-invariant measures and entropy. Featured are Sullivan’s theory of foliation cycles, Plante’s theory of growth of leaves, and the Ghys, Langevin, Walczak theory of geometric entropy. This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. Packed with a wealth of illustrations and copious examples at varying degrees of difficulty, this highly-accessible text offers the first full treatment in the literature of the theory of levels for foliated manifolds of codimension one. It would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations II is Volume 60 in the AMS in the Graduate Studies in Mathematics series.

User’s Reviews

Editorial Reviews: Review “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”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”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 London Mathematical Society From the Publisher “Many exercises … They are well chosen and will keep the interest of a reader on a high level … The book … is a fundamental source for everybody with a serious interest in foliations.”

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