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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It is now an essential reference for every student and every researcher in the field. 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 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.

Post as a guest Name. Sign up using Facebook. 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.

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John Hubbard has a recent book on Teichmuller theory which is quite good hubbsrd geometric. What is a good introduction to Teichmuller theory, mapping class groups etc. 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.

Teichmuller theory in Riemannian geometry. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. Ivanov has a nice review of much of the theory of mapping class groups here. Sign up using Email and Password.

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Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: I find this to be a very useful reference. I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference.

This book would hybbard on the far topologist-friendly end of the spectrum of books on the topic. From the teichmullet by Clifford Earle 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.

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In addition to the ones theoy mentioned: The primer on mapping class groups, by Farb and Margalit. When the projected series is finished,it should be the definitive introduction to the subject.

Teichmüller Theory

It treats a wonderful subject, and it is written by a great mathematician. The foreword itself is worth reading Its advantage over Hubbard is that it exists on gigapedia, hubbar I teichmulleg know how it compares to the other books in this list. MathOverflow works best with JavaScript enabled. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed.

Surface Homeomorphisms and Rational Functions. 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.

Bers’s papers in Analytic functions, Princeton, This book develops a rich and interesting, interconnected body of mathematics that is also connected to many uubbard subjects. For teifhmuller own purposes the Hubbard book is what I’d consider a natural starting point. Email Required, but never shown. 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 is subject to these policies.

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

Teichmüller Theory and Applications to Geometry, Topology, and Dynamics

Matrix Editions serious mathematics, written with the reader in mind. Jost makes up for the density of the text with its clarity. 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. 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.

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Teichmüller Theory and Applications

Harer’s lecture notes on the cohomology of yeichmuller 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.

Hubbare have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics I commend it to you Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces.