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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This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.
What is a good introduction to Teichmuller theory, mapping class groups etc. 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.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. This book would be on the far topologist-friendly end of the spectrum of books on the topic.
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It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually. From the foreword by Clifford Earle It is now an essential reference for every student and every researcher in the field.
When the projected series is finished,it should be the definitive introduction to the subject. Home Questions Tags Users Unanswered. Ivanov has a nice review of much of the theory of mapping class groups here.
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.
Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. Teichmuller theory in Riemannian geometry.
Its advantage over Hubbard is that it exists on gigapedia, but I don’t know how it compares to teichjuller other books in this list. The foreword itself is worth reading For my own purposes the Hubbard book is what I’d consider a natural starting 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.
riemann surfaces – Teichmuller Theory introduction – MathOverflow
Surface Homeomorphisms and Rational Functions. It treats a wonderful subject, and it is written by a great mathematician. 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. If you’re more analytically minded, I recommend Trichmuller and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces.
Teichmuller Theory introduction Ask Question. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. 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.
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. I find this to be a very useful reference.
I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics 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 Bers’s papers in Analytic functions, Princeton, Matrix Editions serious mathematics, written with the reader in mind.
The primer on mapping class groups, by Farb and Margalit.
I only wish that I had had access to a source of this caliber much earlier in my career.
Teichmüller Theory and Applications
Post teivhmuller a guest Name. Sign up using Email and Password. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: