Foliations and the geometry of 3-manifolds / Danny Calegari

This is a book on various subjects related to low-dimensional topology, especially, to 3-maifolds. The main goal (according to the author’s words) is to present a “pseudo-Anosov theory of 3-manifolds." The material covered includes classical as well as recent results, and the objects of study are embedded surfaces, geometric structures, foliations, laminations, homeomorphisms, mapping classes, and other notions related to 3-manifolds. Several notions introduced by Bill Thurston in the last 30 years or so are present in all the theories that are contained in this book, and Thurston’s mark is apparent in almost every page.

The book is extremely well written and it is very pleasant to read. The definitions and the statements of the results are presented clearly, with a lot of illustrations and judicious examples. Of course, part of the results are stated without proofs, but there are also important results that are given with detailed proofs, sometimes due to the the author himself, simplifying or filling some gaps in existing proofs. Some of the results (especially those of Chapter 8) are due to the author.
This book is unique on most of the topics that it contains, and, for this and for other reasons, it constitutes a very important contribution to low-dimensional topology literature. The book will be very useful to anyone working in the subject. (Zentralblatt)

Bibliogr. 343-356. Index