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Yang-Mills Connections on Orientable and Nonorientable Surfaces
Nan-Kuo Ho, National Cheng-Kung University, Taiwan, ROC, and Chiu-Chu Melissa Liu, Northwestern University, Evanston, IL, and Columbia University, New York, NY

Memoirs of the American Mathematical Society
2009; 98 pp; softcover
Volume: 202
ISBN-10: 0-8218-4491-1
ISBN-13: 978-0-8218-4491-5
List Price: US$65
Individual Members: US$39
Institutional Members: US$52
Order Code: MEMO/202/948
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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 \(Sp(n)\).

Table of Contents

  • Introduction
  • Topology of Gauge group
  • Holomorphic principal bundles over Riemann surfaces
  • Yang-Mills connections and representation varieties
  • Yang-Mills \(SO(2n+1)\)-connections
  • Yang-Mills \(SO(2n)\)-connections
  • Yang-Mills \(Sp(n)\)-connections
  • Appendix A. Remarks on Laumon-Rapoport formula
  • Bibliography
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