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On graded bundles and their geometry

Part of the Lecture Notes in Mathematics book series (LNM,volume 838)

Abstract

The notion of a graded bundle is introduced. Although every smooth graded bundle is trivial nevertheless holomorphic graded bundles may not be trivial, i.e. graded elements in their transition functions not always may be all reduced to numbers as it was proved in [7]. The geometry of graded bundles and spaces of graded bundles are explored. It is shown that the differential geometrical construction of Chern classes may be possible only in special cases of graded bundles. The families of graded bundles over instanton solutions of field theory are discussed. A few open problems are mentioned.

Keywords

  • Vector Bundle
  • Line Bundle
  • Chern Class
  • Base Manifold
  • Instanton Solution

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© 1981 Springer-Verlag

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Czyż, J. (1981). On graded bundles and their geometry. In: Ferus, D., Kühnel, W., Simon, U., Wegner, B. (eds) Global Differential Geometry and Global Analysis. Lecture Notes in Mathematics, vol 838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088847

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  • DOI: https://doi.org/10.1007/BFb0088847

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