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.

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

If you’re more analytically minded, I hubbwrd Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces. It treats a wonderful subject, and it is written by a great mathematician. 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. Bers’s papers in Analytic functions, Princeton, Ivanov has a nice review of much of the theory of mapping class groups here.

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 Theeory something, I believe; unfortunately I’m away for the holidays and can’t access Mathscinet to find a precise reference. Its advantage over Hubbard is that it exists on gigapedia, but I don’t know how it heichmuller to the other books in this list. For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces.

Sign up using Facebook. The primer on mapping class groups, by Farb and Margalit.

### Teichmüller Theory and Applications

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 Post as a guest Name. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: Home Questions Tags Users Unanswered. Teichmuller theory in Riemannian geometry.

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 is subject to these policies. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces.

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.

I commend it to you It is now an essential reference for teichmullre student and every researcher in the field. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. Jost makes up for the density of the text with its clarity.

## Teichmüller Theory

John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics When the projected series is finished,it should be the definitive introduction to the subject.

Teiichmuller addition to teichmupler ones already mentioned: This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. 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. It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually. Email Required, but never shown.

Surface Homeomorphisms and Rational Functions. Post Your Answer Discard 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 teichmuloer subject to these policies.

Although the treatment of Teichmuller spaces per se is brief hubbars the book,it contains a wealth of other important topics related to Riemann surfaces.

I find this to be a very useful reference. This book would be on the far topologist-friendly end of the spectrum of books on the topic.

Like everything Jost writes, it’s hybbard clear if compressed within an epsilson of readability. Teichmuller Theory introduction Ask Question.

Matrix Editions serious mathematics, written with the reader in mind. I only wish that I had had access to a teichmullerr of this caliber much earlier in my career.

What is a good introduction to Teichmuller theory, mapping class groups etc. Sign up or log in Sign up using Google. Sign up using Email and Password.