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Yang-Mills Connections on Orientable and Nonorientable Surfaces
 
Nan-Kuo Ho National Cheng-Kung University, Taiwan, ROC
Chiu-Chu Melissa Liu Northwestern University, Evanston, IL and Columbia University, New York, NY
Yang-Mills Connections on Orientable and Nonorientable Surfaces
eBook ISBN:  978-1-4704-0562-5
Product Code:  MEMO/202/948.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
Yang-Mills Connections on Orientable and Nonorientable Surfaces
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Yang-Mills Connections on Orientable and Nonorientable Surfaces
Nan-Kuo Ho National Cheng-Kung University, Taiwan, ROC
Chiu-Chu Melissa Liu Northwestern University, Evanston, IL and Columbia University, New York, NY
eBook ISBN:  978-1-4704-0562-5
Product Code:  MEMO/202/948.E
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $41.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2022009; 98 pp
    MSC: Primary 53; Secondary 58

    In “The Yang-Mills equations over Riemann surfaces”, Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In “Yang-Mills Connections on Nonorientable Surfaces”, the authors study Yang-Mills functional on the space of connections on a principal \(G_{\mathbb{R}}\)-bundle over a closed, connected, nonorientable surface, where \(G_{\mathbb{R}}\) is any compact connected Lie group. In this monograph, the authors generalize the discussion in “The Yang-Mills equations over Riemann surfaces” and “Yang-Mills Connections on Nonorientable Surfaces”. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups \(SO(n)\) and \(Sp(n)\).

  • Table of Contents
     
     
    • Chapters
    • Acknowledgments
    • 1. Introduction
    • 2. Topology of Gauge Group
    • 3. Holomorphic Principal Bundles over Riemann Surfaces
    • 4. Yang-Mills Connections and Representation Varieties
    • 5. Yang-Mills $SO(2n+1)$-Connections
    • 6. Yang-Mills $SO(2n)$-Connections
    • 7. Yang-Mills $Sp(n)$-Connections
    • A. Remarks on Laumon-Rapoport Formula
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2022009; 98 pp
MSC: Primary 53; Secondary 58

In “The Yang-Mills equations over Riemann surfaces”, Atiyah and Bott studied Yang-Mills functional over a Riemann surface from the point of view of Morse theory. In “Yang-Mills Connections on Nonorientable Surfaces”, the authors study Yang-Mills functional on the space of connections on a principal \(G_{\mathbb{R}}\)-bundle over a closed, connected, nonorientable surface, where \(G_{\mathbb{R}}\) is any compact connected Lie group. In this monograph, the authors generalize the discussion in “The Yang-Mills equations over Riemann surfaces” and “Yang-Mills Connections on Nonorientable Surfaces”. They obtain explicit descriptions of equivariant Morse stratification of Yang-Mills functional on orientable and nonorientable surfaces for non-unitary classical groups \(SO(n)\) and \(Sp(n)\).

  • Chapters
  • Acknowledgments
  • 1. Introduction
  • 2. Topology of Gauge Group
  • 3. Holomorphic Principal Bundles over Riemann Surfaces
  • 4. Yang-Mills Connections and Representation Varieties
  • 5. Yang-Mills $SO(2n+1)$-Connections
  • 6. Yang-Mills $SO(2n)$-Connections
  • 7. Yang-Mills $Sp(n)$-Connections
  • A. Remarks on Laumon-Rapoport Formula
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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