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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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. It makes it a wonderfully self-contained resource, but it can also be daunting to someone trying to read it casually.
Teichmüller Theory and Applications to Geometry, Topology, and Dynamics
For connections between hubbxrd these subjects,there’s probably no better current source then Jost’s Compact Riemann Surfaces. When the projected series is finished,it should be the definitive introduction to the subject.
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:. 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. Teichmuller Theory introduction Ask Question. This book would be on the far topologist-friendly end of the spectrum of books on the topic.
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. Post as a guest Name.
Sign up using Facebook. Matrix Editions serious mathematics, written with the reader in mind. From the foreword by Clifford Earle It treats a wonderful subject, and it is written by a great mathematician. 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.
If you’re more analytically minded, I recommend Gardiner and Lakic, Quasiconformal Teichmuller theory and Nag, The complex analytic theory of Teichmuller spaces.
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Surface Homeomorphisms and Rational Functions. This book develops a rich and interesting, interconnected body of mathematics that is also connected to many outside subjects. 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 Sign up or log in Sign up using Google. 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.
I only wish that I had had access to a source of this caliber much earlier in my career. Email Required, but never shown. Like everything Jost writes, it’s crystal clear if compressed within an epsilson of readability.