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Teichmüller Theory

and Applications to Geometry, Topology, and Dynamics
Volume 1: Teichmüller Theory

book cover, Teichmuller theory vol. 2 by John H. Hubbard

with contributions by Adrien Douady, William Dunbar, and Roland Roeder, as well as Sylvain Bonnot, David Brown, Allen Hatcher, Chris Hruska, and Sudeb Mitra and forewords by Clifford Earle and William Thurston

ISBN 9780971576629
Hardcover, 459 pages

2006, $85


Volume 1 of Teichmuller theory has been a joy to read. I have had many epiphanies about the geometry of surfaces as a result of your excellent exposition. And peculiarly, I have learned more from the appendices alone than from many other books. Thank you! -- Meijke Balay, UCLA undergraduate.

You have written the only book on Teichmuller theory that I can understand. -- Professor Steven G. Krantz, Washington University in St. Louis.

I’ve just finished reading your 3-volume Teichmuller theory book. It’s a masterpiece. It’s one of the best math books I’ve ever read, and reading it was sheer pleasure. It’s one of my favorite subjects, and on every topic I thought your coverage was exactly right. -- Professor Danny Calegari, University of Chicago


Introduction in pdf
Table of contents (html)
Table of contents (pdf)
Index(pdf)
Sample pages from each chapter and the appendices (pdf)
Errata and notes
Infrequently asked questions (pdf)

See also

Volume 2: Surface Homeomorphisms and Rational Functions
Volume 3: Manifolds that Fiber over the Circle
Volume 4: Hyperbolization of Haken Manifolds (not yet published)


From the foreword by William Thurston

I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics....This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. I commend it to you....I only wish that I had had access to a source of this caliber much earlier in my career.

Read the complete foreword (pdf)


From the foreword by Clifford Earle

...remarkably self-contained... No other book proves both Royden's theorem about automorphisms of Teichmüller spaces and Slodkowski's theorem about holomorphic motions. But the most important novelty is provided by the author's taste for hands-on geometric constructions and the enthusiasm with which he presents them. (Read more)


Reviews

Zentralblatt MATH:

...an invaluable book. It treats a wonderful subject, and it is written by a great mathematician. It is now an essential reference for every student and every researcher in the field. (complete review)

Mathematical Reviews:

In the volume under review, the author presents Teichmüller theory in order to understand the proofs of Thurston's theorems, but as a result, the book becomes an excellent textbook on Teichmüller theory.

This volume begins with a foreword by Thurston in which the importance and the beauty of Teichmüller theory are discussed from the point of view of his mathematical experiences and his philosophy on mathematics. The foreword itself is worth reading....

In conclusion, the reviewer is convinced that this well-written book will be very useful not only for people who are not familiar with Teichmüller theory, but also for the experts. This is because the reader is offered everywhere in the volume the deep insights of the author, who looks at the topics developed from a new vantage point. (Read more)