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Riemann Surfaces of Infinite Genus
 
Joel Feldman University of British Columbia, Vancouver, BC, Canada
Horst Knörrer Eidgenössische Technische Hochschule, Zurich, Switzerland
Eugene Trubowitz Eidgenössische Technische Hochschule, Zurich, Switzerland
A co-publication of the AMS and Centre de Recherches Mathématiques
Riemann Surfaces of Infinite Genus
Hardcover ISBN:  978-0-8218-3357-5
Product Code:  CRMM/20
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3865-4
Product Code:  CRMM/20.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-3357-5
eBook: ISBN:  978-1-4704-3865-4
Product Code:  CRMM/20.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
Riemann Surfaces of Infinite Genus
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Riemann Surfaces of Infinite Genus
Joel Feldman University of British Columbia, Vancouver, BC, Canada
Horst Knörrer Eidgenössische Technische Hochschule, Zurich, Switzerland
Eugene Trubowitz Eidgenössische Technische Hochschule, Zurich, Switzerland
A co-publication of the AMS and Centre de Recherches Mathématiques
Hardcover ISBN:  978-0-8218-3357-5
Product Code:  CRMM/20
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-1-4704-3865-4
Product Code:  CRMM/20.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-3357-5
eBook ISBN:  978-1-4704-3865-4
Product Code:  CRMM/20.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
  • Book Details
     
     
    CRM Monograph Series
    Volume: 202003; 296 pp
    MSC: Primary 30;

    In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps.

    The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of Kadomcev-Petviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces).

    The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.

    Titles in this series are co-published with the Centre de recherches mathématiques.

    Readership

    Graduate students and research mathematicians interested in analysis and integrable systems.

  • Table of Contents
     
     
    • Chapters
    • $L^2$-cohomology, exhaustions with finite charge and theta series
    • The Torelli Theorem
    • Examples
    • The Kadomcev–Petviashvilli equation
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 202003; 296 pp
MSC: Primary 30;

In this book, the authors geometrically construct Riemann surfaces of infinite genus by pasting together plane domains and handles. To achieve a meaningful generalization of the classical theory of Riemann surfaces to the case of infinite genus, one must impose restrictions on the asymptotic behavior of the Riemann surface. In the construction carried out here, these restrictions are formulated in terms of the sizes and locations of the handles and in terms of the gluing maps.

The approach used has two main attractions. The first is that much of the classical theory of Riemann surfaces, including the Torelli theorem, can be generalized to this class. The second is that solutions of Kadomcev-Petviashvilli equations can be expressed in terms of theta functions associated with Riemann surfaces of infinite genus constructed in the book. Both of these are developed here. The authors also present in detail a number of important examples of Riemann surfaces of infinite genus (hyperelliptic surfaces of infinite genus, heat surfaces and Fermi surfaces).

The book is suitable for graduate students and research mathematicians interested in analysis and integrable systems.

Titles in this series are co-published with the Centre de recherches mathématiques.

Readership

Graduate students and research mathematicians interested in analysis and integrable systems.

  • Chapters
  • $L^2$-cohomology, exhaustions with finite charge and theta series
  • The Torelli Theorem
  • Examples
  • The Kadomcev–Petviashvilli equation
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.