Yang-Mills Connections on Orientable and Nonorientable Surfaces

Studies the 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. 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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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 $Sp(n)$.