Handbook of Teichmuller Theory (IRMA Lectures in Mathematics and Theoretical Physics) (IRMA Lectures in Mathematics and Theoretical Physics, 17) by Athanase Papadopoulos (PDF)

Description

The subject of this handbook is Teichmüller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmüller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned. A publication of the European Mathematical Society. Distributed within the Americas by the American Mathematical Society.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Yesterday, I read 100 pages of this book and it put me right to sleep.What can I say : these are recognized PHD’s. professors and they justhaven’t got into the twenty first century or read an undergrad level text called Indra’s Pearl’s?Teichmüler space was embedded very well by Masket according to Irwin Kra as aT(g,k): dimension=3*g-3+k: g=genus; k=puncture.space as a Riemannian surface that can be generated by Kleinian group limit sets.I just searched the whole book for one decent set of Kleinian group matrices. None found. I searched punctures as well. One diagram of a once punctured torus and a triangulation of a four puncture:T(1,1},T(0,4}.We have here 800 very technical pages on Teichmüler space without one decent definition of a Teichmüller space.And they want in the range of $100 for the text. This book is not fair to a buying public who reads math books.In modern times when nearly everybody has a computer that will run limit set software that is to download free on the internet, not putting examples and pictures in your papers is an arrogant to 19th century move by mathematicians: no excuses : elitism: the attitude or behavior of a person or group who regard themselves as belonging to an elite.

⭐Not found.

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