Yang-Mills connections on orientable and nonorientable surfaces
著者
書誌事項
Yang-Mills connections on orientable and nonorientable surfaces
（Memoirs of the American Mathematical Society, no. 948）
American Mathematical Society, 2009
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注記
"Volume 202, number 948 (second of 5 numbers)."
Includes bibliographical references (p. 97-98)
内容説明・目次
内容説明
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 $Sp(n)$.
目次
- 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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