About: Stable principal bundle

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In mathematics, and especially differential geometry and algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of stability for principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation of earlier work by David Mumford and others on the moduli spaces of vector bundles.

Attributes	Values
rdfs:label	Stable principal bundle (en)
rdfs:comment	In mathematics, and especially differential geometry and algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of stability for principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation of earlier work by David Mumford and others on the moduli spaces of vector bundles. (en)
dcterms:subject	Differential geometry Algebraic geometry Fiber bundles
Wikipage page ID	64244772 (xsd:integer)
Wikipage revision ID	1041695085 (xsd:integer)
Link from a Wikipage to another Wikipage	David Mumford Algebraic group Annamalai Ramanathan Holomorphic vector bundle Riemann surface Differential geometry Mathematics General linear group Tangent bundle Connected space Lie algebra Stable vector bundle Complex Lie group Adjoint bundle G-structure on a manifold Irreducible representation Adjoint representation Algebraic geometry Algebraic varieties Faithful representation Kobayashi–Hitchin correspondence Projective variety Hermite–Einstein connection Algebraic geometry Fiber bundles Chern class Coherent sheaf Higgs bundle Reductive group Differential geometry Associated bundle Indranil Biswas Kähler manifold Vertical and horizontal bundles Vector bundle Principal bundle Nonabelian Hodge correspondence Parabolic subgroup
sameAs	Stable principal bundle Stable principal bundle
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	In mathematics, and especially differential geometry and algebraic geometry, a stable principal bundle is a generalisation of the notion of a stable vector bundle to the setting of principal bundles. The concept of stability for principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation of earlier work by David Mumford and others on the moduli spaces of vector bundles. Many statements about the stability of vector bundles can be translated into the language of stable principal bundles. For example, the analogue of the Kobayashi–Hitchin correspondence for principal bundles, that a holomorphic principal bundle over a compact Kähler manifold admits a Hermite–Einstein connection if and only if it is polystable, was shown to be true in the case of projective manifolds by Subramanian and Ramanathan, and for arbitrary compact Kähler manifolds by Anchouche and Biswas. (en)
prov:wasDerivedFrom	wikipedia-en:Stable_principal_bundle?oldid=1041695085&ns=0
page length (characters) of wiki page	8212 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stable_principal_bundle
is Link from a Wikipage to another Wikipage of	Stable vector bundle Kobayashi–Hitchin correspondence Nonabelian Hodge correspondence
is foaf:primaryTopic of	wikipedia-en:Stable_principal_bundle

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