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