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 |
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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 202; 2009; 98 ppMSC: 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 \(Sp(n)\).
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Table of Contents
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Chapters
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Acknowledgments
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1. Introduction
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2. Topology of Gauge Group
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3. Holomorphic Principal Bundles over Riemann Surfaces
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4. Yang-Mills Connections and Representation Varieties
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5. Yang-Mills $SO(2n+1)$-Connections
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6. Yang-Mills $SO(2n)$-Connections
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7. Yang-Mills $Sp(n)$-Connections
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A. Remarks on Laumon-Rapoport Formula
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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 \(Sp(n)\).
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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
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A. Remarks on Laumon-Rapoport Formula