About: Nonabelian Hodge correspondence

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Nonabelian Hodge correspondence Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FNonabelian_Hodge_correspondence&invfp=IFP_OFF&sas=SAME_AS_OFF

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.

Attributes	Values
rdf:type	Thing
rdfs:label	Nonabelian Hodge correspondence (en)
rdfs:comment	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)
rdfs:seeAlso	Kobayashi–Hitchin correspondence Hermitian Yang–Mills connection Hodge structure
name	Nonabelian Hodge theorem (en)
dcterms:subject	Complex manifolds Vector bundles
Wikipage page ID	46202375 (xsd:integer)
Wikipage revision ID	1109386343 (xsd:integer)
Link from a Wikipage to another Wikipage	Vector-valued differential form De Rham cohomology Complex manifolds Holomorphic vector bundle Hyperkähler manifold Riemann surface Jacobian variety Compact space General linear group Genus (mathematics) Normal subgroup Geometric invariant theory M. S. Narasimhan Simon Donaldson Stable vector bundle Complex algebraic variety Complex differential form Fundamental group Dolbeault operator Gauge transformation Picard group C. S. Seshadri Vector bundles Dolbeault cohomology Irreducible representation Algebraic geometry Nigel Hitchin Gerbe Hitchin's equations Kobayashi–Hitchin correspondence Projective variety Hurewicz theorem Abelian variety Chern class Karen Uhlenbeck Coherent sheaf Hermitian Yang–Mills connection Higgs bundle Hodge theory Holonomy Moduli space Differential geometry Associated bundle Dolbeault theorem Kähler manifold Carlos Simpson Shing-Tung Yau Yang–Mills equations Unitary representation Čech cohomology Complex algebraic varieties Principal bundle Pointed set Stable principal bundle Narasimhan–Seshadri theorem Hermitian metric Sheaf cohomology Glossary of algebraic geometry Semisimple representation Topological space Universal cover Yang–Mills connections Almost complex structure Chern connection Hermitian Yang–Mills equation Reductive algebraic group Structure sheaf Surface group dbr:Kevin_Corlette
sameAs	Nonabelian Hodge correspondence Nonabelian Hodge correspondence
dbp:wikiPageUsesTemplate	dbt:Main_article dbt:Reflist dbt:See_also dbt:Short_description dbt:Math_theorem
has abstract	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)
math statement	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)
prov:wasDerivedFrom	wikipedia-en:Nonabelian_Hodge_correspondence?oldid=1109386343&ns=0
page length (characters) of wiki page	31406 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Nonabelian_Hodge_correspondence
is Link from a Wikipage to another Wikipage of	Nonabelian Hodge theorem Nonabelian Hodge theory Simpson correspondence Complex geometry Stability (algebraic geometry)

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software