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Lectures on Universal Teichmüller Space
 
Armen N. Sergeev Steklov Mathematical Institute, Moscow, Russia
A publication of European Mathematical Society
Front Cover for Lectures on Universal Teichm\"uller Space
Available Formats:
Softcover ISBN: 978-3-03719-141-5
Product Code: EMSSERLEC/19
List Price: $32.00
AMS Member Price: $25.60
Please note AMS points can not be used for this product
Front Cover for Lectures on Universal Teichm\"uller Space
Click above image for expanded view
Lectures on Universal Teichmüller Space
Armen N. Sergeev Steklov Mathematical Institute, Moscow, Russia
A publication of European Mathematical Society
Available Formats:
Softcover ISBN:  978-3-03719-141-5
Product Code:  EMSSERLEC/19
List Price: $32.00
AMS Member Price: $25.60
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Series of Lectures in Mathematics
    Volume: 192014; 111 pp
    MSC: Primary 58; 53;

    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 \(\mathcal{T}\) 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 used to prepare for examinations.

    Readership

    Undergraduate students familiar with basic differential geometry and complex and functional analysis.

  • Request Review Copy
Volume: 192014; 111 pp
MSC: Primary 58; 53;

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 \(\mathcal{T}\) 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 used to prepare for examinations.

Readership

Undergraduate students familiar with basic differential geometry and complex and functional analysis.

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