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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Sign up using Email and Password. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.

What is a good introduction to Teichmuller theory, mapping class groups etc. I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. I find this to be a very useful reference.

Surface Homeomorphisms and Rational Functions. The primer on mapping class groups, by Farb and Margalit. In addition to the ones already mentioned: Post as a guest Name.

This book would be on the far topologist-friendly end of the spectrum of books on the topic. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.

I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. Matrix Editions serious mathematics, written with the reader in mind. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. Surface Homeomorphisms and Rational Functions From the foreword by William Thurston I have long held a great teichmuuller and appreciation for John Hamal Hubbard and his passionate engagement with mathematics Bers’s papers in Analytic teichmupler, Princeton, The foreword itself is worth reading Ivanov has a nice review of much of the theory of mapping class groups here.

MathOverflow works best with JavaScript enabled. 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. I only wish that I had had access to a source of this caliber much earlier in my career.

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. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: 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.

From the foreword by Clifford Earle Home Questions Tags Users Unanswered. Teichmuller Theory introduction Ask Question. Email Required, but never shown.

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

It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually. Sign up using Facebook. 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.

Hubbard’s book is by teichmulller the most readable for the average good student — I don’t think it makes sense to begin with anything else right now. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website teicchmuller subject to these policies.

I commend it to you It treats a wonderful subject, and it is written by a great mathematician. When the projected series is finished,it should be the definitive introduction to the subject.

## Teichmüller Theory

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and heichmuller policyand that your continued use of the website is subject to these policies.

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.

For my own purposes the Hubbard book is what I’d consider a natural starting point. 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.

If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces.

Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces.

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