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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Sign up or log in Sign up using Google. Surface Homeomorphisms and Rational Functions. 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.
For my own purposes the Hubbard book is what I’d consider a natural starting point. 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 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.
Ahlfors, Lectures on quasi-conformal mappings construction of Teichmuller spaces. In addition to the ones already mentioned: When the projected series is finished,it should be the definitive introduction to the subject.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
But the most important novelty is provided by the author’s taste theoey hands-on geometric constructions and the enthusiasm with which he presents them.
This book develops a teivhmuller and interesting, interconnected body of mathematics that is also connected to many outside subjects.
The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. It treats a wonderful subject, and it is written theofy a great mathematician.
John Hubbard has a recent book on Teichmuller theory which is quite yubbard and geometric. I find “An Introduction to Teichmuller spaces” by Imayoshi theofy Taniguchi to be a pretty good 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.
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 is now an essential reference for every student and every researcher in the field. Teichmuller Theory introduction Ask Question. Ivanov has a nice review of much of the theory of mapping class groups here.
Email Required, but never shown. Its a good book, but it builds up alot of technique before it gets to defining Teichmuller spaces. I find this to be a very useful reference. Sign up using Email and Password. What is a good introduction to Teichmuller theory, mapping class groups etc. Sign up using Facebook. Post as a guest Name. Matrix Editions serious mathematics, written with the reader in mind.
The primer on mapping class groups, by Farb and Margalit. Bers’s papers in Analytic functions, Princeton, 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. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.
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Looking at my bookshelf, there’s a few other books that come to mind with varying levels of relevance:. 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.