Vector Calculus, Linear Algebra, and Differential Forms, A Unified Approach (with Barbara Burke Hubbard). Teichmüller Theory and Applications to Geometry. The first volume gave an introduction to Teichmüller theory. Volumes 2 through 4 prove four to Geometry, Topology, and Dynamics. John H. Hubbard 1, 2. Introduction to Teichmüller Theory. Michael Kapovich. August 31, 1 Introduction. This set of notes contains basic material on Riemann surfaces.

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Hubbarf find this to be a very useful hbbard. Hubbard’s book is by far the most readable for the average good student — I don’t think it makes sense to begin with anything else right now.

For my own purposes the Hubbard book is what I’d consider a natural starting point. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces. Jost makes up for the density of the text with its clarity.

Matrix Editions serious mathematics, written with the reader in mind. In addition to the ones already mentioned: For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces. I only wish that I had had access to a source of this caliber much earlier in my career.

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Home Questions Tags Users Unanswered. Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces.

### Teichmüller Theory and Applications

The foreword itself is worth reading Ivanov has a nice review of much of the theory of mapping class groups here. I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics Surface Homeomorphisms and Rational Functions.

From the foreword by Clifford Earle I commend it to you Bers’s papers in Analytic functions, Princeton, If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces.

Harer’s lecture notes on the cohomology of moduli spaces doesn’t have all the proofs, but describes the main ideas related to the cell decomposition of the moduli spaces; Springer LNM something, I believe; unfortunately I’m away for the holidays and can’t access Mathscinet to find a precise reference.

Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:.

### Archive ouverte HAL – Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

Email Required, but never shown. MathOverflow works best with JavaScript enabled. Surface Homeomorphisms and Rational Functions 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 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. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed.

When the projected series is finished,it should be the definitive introduction to the subject.

## Teichmüller Theory

Its advantage over Hubbard is that it exists on gigapedia, but I don’t know how it compares to the other books in this list.

The primer on mapping class groups, by Farb and Margalit.

Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. This book would be on the far topologist-friendly end of the spectrum of books on the topic.

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## Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. This teichjuller 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. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.

Sign up using Facebook. Post as a guest Name. Teichmuller Theory introduction Ask Question. I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually. Although the treatment of Teichmuller spaces per se is brief in the book,it contains a wealth of other important topics related to Riemann surfaces.

Sign up using Email and Password. Teichmuller theory in Riemannian geometry. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. What is a good introduction to Teichmuller theory, mapping class groups etc. 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.