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

For my own purposes the Hubbard book is what I’d consider a natural starting point. If you’re more analytically minded, I theoyr Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory hubbad Teichmuller spaces. Home Questions Tags Users Unanswered. 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. Ivanov has a nice review of much of the theory of mapping class groups here.

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 teichumller John Hamal Hubbard and his passionate engagement with mathematics Matrix Editions serious mathematics, written with the reader in mind.

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

This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. In addition to the ones already mentioned: Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.

The foreword itself is worth reading When the projected series is finished,it should be the definitive introduction to the subject. Sign up using Email and Password.

Teichmuller Theory introduction Ask Question. The primer on mapping class groups, by Farb and Margalit. What is a good introduction to Teichmuller theory, mapping class groups etc. teichmulller

Email Required, tueory never shown. John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. Sign up or log in Sign up using Google.

Jost makes up for the density of the text with its clarity. For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces.

### “And don’t call me Shirley”

I find this to be a very useful reference. 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 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.

Teichmuller theory in Riemannian geometry. Bers’s papers in Analytic functions, Teichmmuller, I commend it to you Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces.

Although teichmuller treatment of Teichmuller spaces per se is brief in the book,it contains a wealth of other important topics related to Riemann surfaces. Surface Homeomorphisms and Rational Functions.

### riemann surfaces – Teichmuller Theory introduction – MathOverflow

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Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces. This book would be on the far topologist-friendly end of the spectrum of books on the topic. I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. Teichmmuller Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our hheory terms of serviceprivacy policy and cookie policyand that your continued use of the theofy is subject to these policies.

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.

From the foreword by Clifford Earle It makes it a wonderfully self-contained resource, but it can thepry be daunting to someone trying to read it casually.

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policy hteory, and our Terms of Service. It is now an essential reference for every student and every researcher in the field. Sign up using Facebook. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed.

I only wish that I had had access to a source of this caliber much earlier in my career. MathOverflow works best with JavaScript enabled. It treats a wonderful subject, and it is written by a great mathematician.