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- In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold. The theorem can be considered a vast generalisation of the Narasimhan–Seshadri theorem which defines a correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri theorem may be obtained as a special case of the nonabelian Hodge correspondence by setting the Higgs field to zero. (en)
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- 31406 (xsd:nonNegativeInteger)
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- A Higgs bundle has a Hermitian Yang–Mills metric if and only if it is polystable. This metric is a harmonic metric, and therefore arises from a semisimple representation of the fundamental group, if and only if the Chern classes and vanish. Furthermore, a Higgs bundle is stable if and only if it admits an irreducible Hermitian Yang–Mills connection, and therefore comes from an irreducible representation of the fundamental group. (en)
- There are homeomorphisms of moduli spaces which restrict to homeomorphisms . (en)
- A Higgs bundle arises from a semisimple representation of the fundamental group if and only if it is polystable. Furthermore it arises from an irreducible representation if and only if it is stable. (en)
- A representation of the fundamental group is semisimple if and only if the flat vector bundle admits a harmonic metric. Furthermore the representation is irreducible if and only if the flat vector bundle is irreducible. (en)
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- Nonabelian Hodge theorem (en)
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- In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after and Carlos Simpson) is a correspondence between Higgs bundles and representations of the fundamental group of a smooth, projective complex algebraic variety, or a compact Kähler manifold. (en)
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- Nonabelian Hodge correspondence (en)
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