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- W2964339232 abstract "We define Hitchin’s moduli space for a principal bundle P, whose structure group is a compact semisimple Lie group K, over a compact non-orientable Riemannian manifold M. We use the Donaldson–Corlette correspondence, which identifies Hitchin’s moduli space with the moduli space of flat connections, which remains valid when M is non-orientable. This enables us to study Hitchin’s moduli space both by gauge theoretical methods and algebraically by using representation varieties. If the orientable double cover M~ of M is a Kahler manifold with odd complex dimension and if the Kahler form is odd under the non-trivial deck transformation τ on M~, Hitchin’s moduli space of the pull-back bundle has a hyper-Kahler structure and admits an involution induced by τ. The fixed-point set is symplectic or Lagrangian with respect to various symplectic structures on the moduli space. We compare the gauge theoretical constructions with the algebraic approach using representation varieties." @default.
- W2964339232 created "2019-07-30" @default.
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- W2964339232 date "2018-01-01" @default.
- W2964339232 modified "2023-10-01" @default.
- W2964339232 title "Hitchin’s equations on a nonorientable manifold" @default.
- W2964339232 doi "https://doi.org/10.4310/cag.2018.v26.n4.a6" @default.
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