Lectures on Universal Teichmüller Space
By:Armen Sergeev
Published on 2014 by Erich Schmidt Verlag GmbH & Co. KG
This book is based on a lecture course given by the author at the Educational Center of the Steklov Mathematical Institute in 2011. It is designed for a one-semester course for undergraduate students familiar with basic differential geometry and complex and functional analysis. The universal Teichmüller space T is the quotient of the space of quasisymmetric homeomorphisms of the unit circle modulo Möbius transformations. The first part of the book is devoted to the study of geometric and analytic properties of T. It is an infinite-dimensional Kähler manifold which contains all classical Teichmüller spaces of compact Riemann surfaces as complex submanifolds, which explains the name |universal Teichmüller space|. Apart from classical Teichmüller spaces, T contains the space S of diffeomorphisms of the circle modulo Möbius transformations. The latter space plays an important role in the quantization of the theory of smooth strings. The quantization of T is presented in the second part of the book. In contrast with the case of diffeomorphism space S, which can be quantized in frames of the conventional Dirac scheme, the quantization of T requires an absolutely different approach based on the noncommutative geometry methods. The book concludes with a list of 24 problems and exercises which can used to prepare for examinations.
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Book ID of Lectures on Universal Teichmüller Space's Books is Cada76etozEC, Book which was written byArmen Sergeevhave ETAG "zKq5OWUYlI8"
Book which was published by Erich Schmidt Verlag GmbH & Co. KG since 2014 have ISBNs, ISBN 13 Code is 9783037191415 and ISBN 10 Code is 3037191414
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