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 this to be a very useful reference. For my own purposes the Hubbard book is what I’d consider a natural starting point. Surface Homeomorphisms and Rational Functions. 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.
When the projected series is finished,it should be the definitive introduction to the subject. I commend it to you It treats a wonderful subject, and it is written by a great mathematician.
I huhbard “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. This book would be on the far topologist-friendly end of the spectrum of books on the topic. This book develops a hubbarrd and interesting, interconnected body of mathematics that is also connected to many outside subjects. 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 From the foreword by Clifford Earle Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:.
Ivanov has a nice review of much of the theory of mapping class groups hubbarr. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. The primer on mapping class groups, by Farb and Margalit. Post as a guest Name. Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces. In addition to the ones already mentioned: 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.
Sign thory or log in Sign up using Google. John Hubbard has a recent book on Teichmullwr theory which is quite good and geometric.
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.
It makes it a wonderfully self-contained resource, but it can also hkbbard daunting to someone trying to read it casually.
Teichmüller Theory and Applications
Its theeory good book, but it builds up alot of technique before it gets to defining Teichmuller spaces. Teichmuller Theory introduction Ask Question. I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics 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.
I only wish that I had had access to a source of this caliber much earlier in my career. The foreword itself is worth reading Its advantage over Hubbard is that it exists on gigapedia, but I don’t know how it compares to the hjbbard books in this list.
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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 emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. Bers’s papers in Analytic functions, Princeton,