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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riemann surfaces – Teichmuller Theory introduction – MathOverflow
Matrix Editions serious mathematics, written with the reader in mind. It makes teochmuller a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually.
The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. It is now an essential reference for every student and every researcher in the field. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces. 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 only wish that I had had access to a source of this caliber much earlier in my career. Ivanov has a teichmuller review of much of the theory of mapping class groups hubbaard.
hubard Hubbard’s book is by far the most readable for the average good student — I hubbarv 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:. In addition to the ones already mentioned: Teichmuller Theory introduction Ask Question. If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces. The foreword itself is worth reading Teichmuller theory in Riemannian geometry. Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces.
Bers’s teochmuller in Analytic functions, Princeton, It treats a wonderful subject, and it is written by a great mathematician. Jost makes up for the density of the text with its clarity. Sign up using Facebook. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.
I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference. I commend it to you Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: Surface Homeomorphisms and Rational Functions.
Email Required, but never shown. 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. Post as a guest Name.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
When the projected series is finished,it should be the definitive introduction to the subject. But the most important novelty is provided by the author’s taste for hands-on teichmulldr constructions and the enthusiasm with which he presents them.
This book would be on the far topologist-friendly end of the spectrum of books on the topic. For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces.
Teichmüller Theory and Applications
Home Questions Tags Users Unanswered. John Hubbard has a recent book on Teichmuller theory which is quite good and geometric. Sign hubbxrd using Email and Password. I find this to be a very useful reference. Harer’s lecture notes on the cohomology of moduli spaces doesn’t have all the proofs, but describes the teichmluler 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.