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Lectures on Universal Teichmüller Space

Sergeev, Armen,

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Lectures on Universal Teichmüller Space

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on Universal Teichmüller Space/ Armen Sergeev
作者:	Sergeev, Armen,
出版者:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
面頁冊數:	1 online resource (111 pages)
標題:	Calculus & mathematical analysis -
電子資源:	https://doi.org/10.4171/141
電子資源:	https://www.ems-ph.org/img/books/sergeev_mini.gif
ISBN:	9783037196410

Lectures on Universal Teichmüller Space
Sergeev, Armen,

Lectures on Universal Teichmüller Space[electronic resource] /Armen Sergeev - Zuerich, Switzerland :European Mathematical Society Publishing House,2014 - 1 online resource (111 pages) - EMS Series of Lectures in Mathematics (ELM) ;2523-5176.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

This book is based on a lecture course given by the author at the Educational Center of Steklov Mathematical Institute in 2011. It is designed for a one semester course for undergraduate students, familiar with basic differential geometry, complex and functional analysis. The universal Teichmüller space $\mathcal T$ 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 $\mathcal T$. 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, $\mathcal T$ contains the space $\mathcal S$ 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 $\mathcal T$ is presented in the second part of the book. In contrast with the case of diffeomorphism space $\mathcal S$, which can be quantized in frames of the conventional Dirac scheme, the quantization of $\mathcal T$ requires an absolutely different approach based on the noncommutative geometry methods. The book concludes with a list of 24 problems and exercises which can be used during the examinations.

ISBN: 9783037196410

Standard No.: 10.4171/141doiSubjects--Topical Terms:

3480907
Calculus & mathematical analysis

Lectures on Universal Teichmüller Space
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