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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Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces.
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. It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually.
Email Required, but never shown. 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.
Surface Homeomorphisms and Rational Functions From the foreword by Teichmukler Thurston I have long held a great admiration teeichmuller appreciation for John Hamal Hubbard and his passionate engagement with mathematics 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 develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects.
Teichmüller Theory and Applications
If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces. Sign up using Email and Password. This book would be on the far topologist-friendly end of the spectrum of books on the topic. Matrix Editions serious mathematics, written with the reader in mind. I find “An Introduction to Teichmuller spaces” by Imayoshi and Taniguchi to be a pretty good reference.
For connections between all these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces. Home Questions Tags Users Unanswered. For my own purposes the Hubbard book is what I’d consider a natural starting point.
Looking at my bookshelf, hubbagd a few other books that come to mind with varying levels of relevance: What is a good introduction to Teichmuller theory, mapping class groups etc.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
It treats a wonderful subject, and it is written by a great mathematician. The theroy itself is worth reading 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.
From the foreword by Clifford Earle I only wish that I had had access to a source of this caliber much earlier in my career. 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. Teichmuller Theory introduction Ask Question. 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.
Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability. The emphasis is on mapping class groups rather teihcmuller Teichmuller theory, but the latter is certainly discussed.
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Sign up using Facebook. I find this to be a very useful reference.
I commend it to you Bers’s papers in Analytic functions, Princeton,