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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I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. By clicking “Post Huubbard Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Sign up using Facebook. From the foreword by Clifford Earle 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. I commend it to you 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.

Bers’s papers in Analytic functions, Princeton, Teichmuller Theory introduction Ask Question.

Teichmüller Theory and Applications

Surface Homeomorphisms and Rational Functions. Jost makes up for the density of the text with its clarity. Sign up or log in Sign up using Google. I find this to be a very useful reference. Home Questions Tags Users Unanswered.

Teichmuller theory in Riemannian geometry. John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces.


If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces. It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually.

Teichmüller Theory

Post as a guest Name. The foreword itself is worth reading This book would be on the far topologist-friendly end of the spectrum of books on the topic. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.

Teichhmuller has a nice review of much of the theory of mapping class groups here. MathOverflow works best with JavaScript enabled.

For my own teicumuller the Hubbard book is what I’d consider a natural starting point. What is a good introduction to Teichmuller theory, mapping class groups etc.

I only wish that I had had access to a source of this caliber much earlier in my career. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.

When the projected series is finished,it should be the definitive introduction to the subject. Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. In addition to the ones already mentioned: 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.


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.

The primer on mapping class groups, by Farb and Margalit. 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: I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces.

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. 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. Email Required, but never shown.