東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Lectures on Universal Teichmüller Space

Sergeev, Armen,

Linked to FindBook

Google Book

Amazon

博客來

Lectures on Universal Teichmüller Space

Record Type:	Electronic resources : Monograph/item
Title/Author:	Lectures on Universal Teichmüller Space/ Armen Sergeev
Author:	Sergeev, Armen,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2014,
Description:	1 online resource (111 pages)
Subject:	Calculus & mathematical analysis -
Online resource:	https://doi.org/10.4171/141
Online resource:	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
LDR:02437nmm a22003015a 4500 001 2233264
003 CH-001817-3
005 20140812234500.0
006 a fot ||| 0|
007 cr nn mmmmamaa
008 210928e20140812sz fot ||| 0|eng d
020 $a 9783037196410
024 7 0 $a 10.4171/141 $2 doi
035 $a 183-140812
040 $a ch0018173
072 7 $a PBK $2 bicssc
084 $a 58-xx $a 53-xx $2 msc
100 1 $a Sergeev, Armen, $e author. $3 3481086
245 1 0 $a Lectures on Universal Teichmüller Space $h [electronic resource] / $c Armen Sergeev
260 3 $a Zuerich, Switzerland : $b European Mathematical Society Publishing House, $c 2014
300 $a 1 online resource (111 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 0 $a EMS Series of Lectures in Mathematics (ELM) ; $x 2523-5176
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $a 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.
650 0 7 $a Calculus & mathematical analysis $2 bicssc $3 3480907
650 0 7 $a Global analysis, analysis on manifolds $2 msc $3 3480808
650 0 7 $a Differential geometry $2 msc $3 3480811
856 4 0 $u https://doi.org/10.4171/141
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/sergeev_mini.gif