Correspondsnce between Higgs bundles and fundamental group representations
In algebraic geometry and differential geometry, the nonabelian Hodge correspondence or Corlette–Simpson correspondence (named after Kevin Corlette 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.
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geometry, the nonabelianHodgecorrespondence or Corlette–Simpson correspondence (named after Kevin Corlette and Carlos Simpson) is a correspondence between...
of the Calabi conjecture, the Hitchin–Kobayashi correspondence, the nonabelianHodgecorrespondence, and existence results for Kähler–Einstein metrics...
vector bundle, where the derivative is scaled to zero. The nonabelianHodgecorrespondence says that, under suitable stability conditions, the category...
of the fundamental lemma. Yang–Mills equations Higgs bundle NonabelianHodgecorrespondence Character variety Hitchin's equations Chudnovsky, D.V. (1979)...
Simpson and Pierre Deligne. Simpson was an Invited Speaker with talk NonabelianHodge theory at the International Congress of Mathematicians in 1990 at Kyoto...
was shown by Anchouche and Biswas that the analogue of the nonabelianHodgecorrespondence for Higgs vector bundles is true for principal G {\displaystyle...
Lefschetz pencils). Jean Giraud worked out torsor theory extensions of nonabelian cohomology there as well. Many others such as David Mumford, Robin Hartshorne...
that their automorphism groups may be infinite, discrete, and highly nonabelian. By a version of the Torelli theorem, the Picard lattice of a complex...
of the base space M, the principal bundle P, and the gauge group G. In nonabelian Yang–Mills theories, D F = 0 {\displaystyle DF=0} and D ∗ F = 0 {\displaystyle...
group systems by Blakers), after a suggestion of Samuel Eilenberg: A nonabelian generalization of chain complexes of abelian groups which are equivalent...
(1921–2016), mathematical logic Boaz Tsaban (born 1973), set theory and nonabelian cryptology Boris Tsirelson (1950–2020), probability theory and functional...
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