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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For my own purposes the Hubbard book is what I’d consider a natural starting point. What is a good introduction to Teichmuller theory, mapping class groups etc.
Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance: The primer on mapping class groups, by Farb and Margalit. This is because the reader is theody everywhere in the volume the deep insights of the author, who looks at the topics developed from a new vantage point.
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Hubbard’s book is by jubbard the most readable for the average good student — I don’t think it makes sense to begin teichmullerr anything else right now. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. Sign up using Facebook. Jost makes up for the density of the text with its clarity. John Hubbard has a recent book on Teichmuller theory which is quite good and geometric.
riemann surfaces – Teichmuller Theory introduction – MathOverflow
I only wish that I had had access to a source of this caliber much earlier in my career. I find this to be a very useful reference.
Email Required, but never shown. 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.
In addition to the ones already mentioned: Matrix Editions serious mathematics, written with the reader in mind. The foreword itself is worth reading 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.
The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. Ivanov has a nice review of much of the theory of mapping class groups here. Sign up or log in Sign up using Google. Bers’s papers in Analytic functions, Princeton, I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference.
Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. Teichmuller Theory introduction Ask Question. If you’re more analytically minded, Theorh recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces.
Sign up using Email and Password. I commend it to you Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. When the projected series is finished,it should be the definitive introduction to the subject. Home Questions Tags Users Unanswered.
Teichmüller Theory and Applications
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. This book would be on the far topologist-friendly end of the spectrum of books on the topic.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
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. For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces. Teichmuller theory in Riemannian geometry. Surface Homeomorphisms and Rational Functions.