Teichmüller
Theory and Applications to Geometry, Topology, and Dynamics
Volume I: Teichmüller
Theory
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
with
forewords by Clifford Earle and William Thurston
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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 entire foreword
From the
foreword to volume 1 by Clifford Earle:
...remarkably selfcontained... 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 handson geometric constructions and
the enthusiasm with which he presents them.
see the
complete foreword
From the review in 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.
see the
complete review
From the MAA review:
There is an ambitious new publishing house on the mathematics scene,
Matrix Editions, with lead author John H. Hubbard. As a motto, Matrix
Editions has chosen "Serious mathematics, written with the reader in
mind." The volume under review is the first volume of a
twovolume book. It beautifully exemplifies the motto.
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From 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 wellwritten 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.
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From the author's preface:
Between 1970 and 1980, William Thurston astonished
the mathematical world by announcing the four theorems discussed in
this book:
 The
classification of homeomorphisms of surfaces.
 The
topological characterization of rational maps.
 The
hyperbolization theorem for 3manifolds that fiber over the circle.
 The
hyperbolization theorem for Haken 3manifolds.
Not only are the theorems of extraordinary beauty in themselves, but
the methods of proof Thurston introduced were so novel and displayed
such amazing geometric insight that to this day they have barely
entered the accepted methods of mathematicians in the field.
....
The book is divided into two volumes. The first
sets up the Teichmüller theory necessary for discussing
Thurston's theorems; the second proves Thurston's theorems, providing
more background material where
necessary, in particular for the two hyperbolization theorems.
....
I have tried very hard to make this book
accessible to a secondyear graduate student: I am assuming the results
of a pretty solid first year of graduate studies, but very little
beyond, and I have included appendices with proofs of anything not
ordinarily in such courses. I never refer to the
literature for some difficult but important result. Such references are
the bane of readers, who often find the sight differences of
assumptions and incompatible notations an insurmountable obstacle.
complete
preface in html, including list of prerequisites
complete
preface in pdf, including list of prerequisites
Front
cover (designed
by Leila Joiner)
table of
contents (html)
table of
contents (pdf)
index (in
pdf)
Samples pages from each chapter and the appendices
Errata and notes
Infrequently
asked questions (pdf)
Order
information: books shipped within the United States
Order
information: other countries
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