Invariant connections and invariant holomorphic bundles on homogeneous manifolds

• Autorzy: Indranil Biswas , Andrei Teleman
• Języki publikacji: EN

Abstrakty

EN

Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).

Słowa kluczowe

EN

Invariant connection; Gauge group; Principal bundle

Kategorie tematyczne

• 53C05: Connections, general theory
• 32L05: Holomorphic bundles and generalizations
• 53B35: Hermitian and K\"ahlerian structures

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 1
• Strony: 1-13

Daty

wydano

2014-01-01

online

2013-10-30

Twórcy

autor

Indranil Biswas

• Tata Institute of Fundamental Research

autor

Andrei Teleman

• Aix-Marseille Université

Bibliografia

• [1] Biswas I., Homogeneous principal bundles over the upper half-plane, Kyoto J. Math., 2010, 50(2), 325–363 http://dx.doi.org/10.1215/0023608X-2009-016
• [2] Biswas I., Classification of homogeneous holomorphic hermitian principal bundles over G/K, Forum Math. (in press), DOI: 10.1515/forum-2012-0131
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• [10] Lübke M., Teleman A., The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds, Mem. Amer. Math. Soc., 183(863), American Mathematical Society, Providence, 2006
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Identyfikatory

DOI

10.2478/s11533-013-0330-9