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2014 | 12 | 1 | 1-13
Tytuł artykułu

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

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Warianty tytułu
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
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
1
Strony
1-13
Opis fizyczny
Daty
wydano
2014-01-01
online
2013-10-30
Twórcy
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
  • [3] Chevalley C., Eilenberg S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc., 1948, 63(1), 85–124 http://dx.doi.org/10.1090/S0002-9947-1948-0024908-8
  • [4] Donaldson S.K., Kronheimer P.B., The Geometry of Four-Manifolds, Oxford Math. Monogr., Oxford University Press, New York, 1990
  • [5] Greub W., Halperin S., Vanstone R., Connections, Curvature, and Cohomology, II, Pure Appl. Math., 47-II, Academic Press, New York-London, 1973
  • [6] Hofmann K.H., Morris S.A., The Structure of Compact Groups, 2nd ed., de Gruyter Stud. Math., 25, Walter de Gruyter, Berlin, 2006
  • [7] Husemoller D., Fibre Bundles, 3rd ed., Grad. Texts in Math., 20, Springer, New York, 1994 http://dx.doi.org/10.1007/978-1-4757-2261-1
  • [8] Kobayashi S., Nomizu K., Foundations of Differential Geometry, I, Interscience Tracts in Pure and Applied Mathematics, 15(I), Interscience, New York-London, 1963
  • [9] Kobayashi S., Nomizu K., Foundations of Differential Geometry, II, Interscience Tracts in Pure and Applied Mathematics, 15(II), Interscience, New York-London, 1969
  • [10] Lübke M., Teleman A., The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds, Mem. Amer. Math. Soc., 183(863), American Mathematical Society, Providence, 2006
  • [11] Wang H., On invariant connections over a principal fibre bundle, Nagoya Math. J., 1958, 13, 1–19
  • [12] Yang K., Almost Complex Homogeneous Spaces and their Submanifolds, World Scientific, Singapore, 1987
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0330-9
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