Teichmuller Theory introduction - MathOverflow

Teichmuller Theory introduction

2010-01-02T20:01:31Z

What is a good introduction to Teichmuller theory, mapping class groups etc., and relation to moduli space of curves or Riemann surfaces?

Answer by Matt Noonan for Teichmuller Theory introduction

2010-01-02T20:13:00Z

John Hubbard has a recent book on Teichmuller theory which is quite good and geometric.

Answer by Sam Nead for Teichmuller Theory introduction

2010-01-02T20:31:34Z

The primer on mapping class groups, by Farb and Margalit.

Answer by algori for Teichmuller Theory introduction

2010-01-02T21:04:23Z

In addition to the ones already mentioned:

J. 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).

K. Strebel, Quadratic differentials (careful exposition of the complex analytic results used to construct the cell decomposition mentioned above; not much about moduli spaces or Teichm\"uller theory though; Springer Erbebnisse).

L. Ahlfors, Lectures on quasi-conformal mappings (construction of Teichmuller spaces).

L. Ahlfors' and L. Bers's papers in Analytic functions, Princeton, 1960.

Answer by Richard Kent for Teichmuller Theory introduction

2010-01-02T22:31:42Z

If you're more analytically minded, I recommend

Gardiner and Lakic, Quasiconformal Teichmuller theory

and

Nag, The complex analytic theory of Teichmuller spaces

Answer by Ilya Grigoriev for Teichmuller Theory introduction

2010-01-02T23:23:21Z

I find "An Introduction to Teichmuller spaces" by Imayoshi and Taniguchi to be a pretty good reference. 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.

Answer by Ryan Budney for Teichmuller Theory introduction

2010-01-04T19:08:31Z

Looking at my bookshelf, there's a few other books that come to mind with varying levels of relevance:

Ahlfors & Sario. Riemann Surfaces.

Jost. Compact Riemann Surfaces.

Maskit. Kleinian Groups.

Tromba. Teichmuller theory in Riemannian geometry.

Farkas and Kra. Riemann Surfaces.

For my own purposes the Hubbard book is what I'd consider a natural starting point.

Answer by Andrew L for Teichmuller Theory introduction

2010-07-06T07:15:53Z

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. When the projected series is finished,it should be the definitive introduction to the subject.

For connections between all these subjects,there's probably no better current source then Jost's Compact Riemann Surfaces. 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. Like everything Jost writes, it's crystal clear if compressed within an epsilson of readability. Jost makes up for the density of the text with its clarity.

Answer by Jeffrey Giansiracusa for Teichmuller Theory introduction

2010-07-06T15:06:47Z

Ivanov has a nice review of much of the theory of mapping class groups here. The emphasis is on mapping class groups rather than Teichmuller theory, but the latter is certainly discussed. I find this to be a very useful reference.

Answer by Chris Judge for Teichmuller Theory introduction

2011-08-03T21:13:34Z

McMullen's notes (http://www.math.harvard.edu/~ctm/home/text/class/harvard/275/09/html/base/rs/rs.pdf)