About: Higgs bundle

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In mathematics, a Higgs bundle is a pair consisting of a holomorphic vector bundle E and a Higgs field , a holomorphic 1-form taking values in the bundle of endomorphisms of E such that . Such pairs were introduced by Nigel Hitchin, who named the field after Peter Higgs because of an analogy with Higgs bosons. The term 'Higgs bundle', and the condition (which is vacuous in Hitchin's original set-up on Riemann surfaces) was introduced later by Carlos Simpson.

Attributes	Values
rdf:type	place yago:WikicatComplexManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	Higgs-Bündel (de) Higgs bundle (en)
rdfs:comment	In der Mathematik sind Higgs-Bündel ein Hilfsmittel in der Darstellungstheorie von Flächengruppen und Fundamentalgruppen komplexer Mannigfaltigkeiten. Sie wurden von Nigel Hitchin eingeführt und wegen der Analogie zu Higgs-Bosonen nach Peter Higgs benannt. (de) In mathematics, a Higgs bundle is a pair consisting of a holomorphic vector bundle E and a Higgs field , a holomorphic 1-form taking values in the bundle of endomorphisms of E such that . Such pairs were introduced by Nigel Hitchin, who named the field after Peter Higgs because of an analogy with Higgs bosons. The term 'Higgs bundle', and the condition (which is vacuous in Hitchin's original set-up on Riemann surfaces) was introduced later by Carlos Simpson. (en)
dcterms:subject	Complex manifolds Vector bundles
Wikipage page ID	34143255 (xsd:integer)
Wikipage revision ID	1122721216 (xsd:integer)
Link from a Wikipage to another Wikipage	Complex manifolds Holomorphic vector bundle Peter Higgs Riemann surface Mathematics SU(2) Gauge theory Notices of the American Mathematical Society Fundamental group Vector bundles Affine connection Hitchin's equations Hitchin system Journal of Differential Geometry Projective variety Kähler manifold Carlos Simpson Category (mathematics) Higgs field Principal bundle Nonabelian Hodge correspondence Compact (mathematics)
Link from a Wikipage to an external page	https://www.ams.org/notices/200708/tx070800980p.pdf
sameAs	Higgs bundle Higgs bundle Higgs bundle Higgs bundle Higgs bundle
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Cite_journal dbt:Ref dbt:Reflist dbt:Short_description dbt:Harvs dbt:Topology-stub
first	Nigel (en)
last	Hitchin (en)
year	1987 (xsd:integer)
has abstract	In der Mathematik sind Higgs-Bündel ein Hilfsmittel in der Darstellungstheorie von Flächengruppen und Fundamentalgruppen komplexer Mannigfaltigkeiten. Sie wurden von Nigel Hitchin eingeführt und wegen der Analogie zu Higgs-Bosonen nach Peter Higgs benannt. (de) In mathematics, a Higgs bundle is a pair consisting of a holomorphic vector bundle E and a Higgs field , a holomorphic 1-form taking values in the bundle of endomorphisms of E such that . Such pairs were introduced by Nigel Hitchin, who named the field after Peter Higgs because of an analogy with Higgs bosons. The term 'Higgs bundle', and the condition (which is vacuous in Hitchin's original set-up on Riemann surfaces) was introduced later by Carlos Simpson. A Higgs bundle can be thought of as a "simplified version" of a flat holomorphic connection on a holomorphic vector bundle, where the derivative is scaled to zero. The nonabelian Hodge correspondence says that, under suitable stability conditions, the category of flat holomorphic connections on a smooth, projective complex algebraic variety, the category of representations of the fundamental group of the variety, and the category of Higgs bundles over this variety are actually equivalent. Therefore, one can deduce results about gauge theory with flat connections by working with the simpler Higgs bundles. (en)
author-link	Nigel Hitchin (en)
gold:hypernym	Pair
prov:wasDerivedFrom	wikipedia-en:Higgs_bundle?oldid=1122721216&ns=0
page length (characters) of wiki page	4336 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Higgs_bundle
is Link from a Wikipage to another Wikipage of	Character variety Gauge theory (mathematics) Complex geometry Ginzburg–Landau theory Nigel Hitchin Hitchin's equations Hitchin system Kobayashi–Hitchin correspondence Higgs mechanism Carlos Simpson Yang–Mills equations Stable principal bundle Nonabelian Hodge correspondence Hitchin moduli space Hitchin pair
is Wikipage redirect of	Hitchin moduli space Hitchin pair
is known for of	Nigel Hitchin
is known for of	Nigel Hitchin
is foaf:primaryTopic of	wikipedia-en:Higgs_bundle

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