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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Bers’s papers in Analytic functions, Princeton, I find this to be a very useful reference.
Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces. I have long held a great admiration and appreciation for John Hamal Hubbard and his passionate engagement with mathematics This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. For my own purposes the Hubbard book is what I’d consider a natural starting point.
It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually. Sign up using Facebook. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: Email Required, but never shown. Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. This book would be on the far topologist-friendly end of the spectrum of books on the topic.
What is a good introduction to Teichmuller theory, mapping class groups etc.
For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces. Ivanov has a nice review of much of the theory of mapping class groups here. 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.
Teichmuller theory in Riemannian geometry. I commend it to you If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of 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. The foreword itself is worth reading The primer on mapping class groups, by Farb and Margalit. Sign up or log in Sign up using Google. It is now an essential reference for every student and every researcher in the field.
The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.
Sign up using Email and Password. Surface Homeomorphisms and Rational Functions. 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. Matrix Editions serious mathematics, written with the reader in mind. John Hubbard has a recent book on Teichmuller theory which is quite good and geometric.
It treats a wonderful subject, and it is written by a great mathematician. Post as a guest Name. From the foreword by Clifford Earle In addition to the ones already mentioned: I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference.
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.
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. When the projected teichmhller is finished,it should be the definitive introduction to the subject.
I only wish that I had had access to a source of this caliber much earlier in my career.