• Title, Summary, Keyword: vector bundles

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LIMITS OF TRIVIAL BUNDLES ON CURVES

  • Ballico, Edoardo
    • Communications of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.43-61
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    • 2020
  • We extend the work of A. Beauville on rank 2 vector bundles on a smooth curve in several directions. We give families of examples with large dimension, add new existence and non-existence results and prove the existence of indecomposable limits with arbitrary rank. To construct the large dimensional families we use the examples of limits of rank 2 trivial bundles on ℙ2 and ℙ3 due to C. Banica. We also consider a more flexible notion: limits of trivial bundles on nearby curves.

Vector Bundles on Curves with Many "spread" Sections

  • Ballico, E.
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.167-169
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    • 2005
  • Here we introduce and study vector bundles, E, on a smooth projective curve X having many "spread" sections and for which $E^{*}\;{\otimes}{\omega}X$ has many "spread" sections. We show that no such bundle exists on X if the gonality of X is too low.

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DEFINABLE Cr FIBER BUNDLES AND DEFINABLE CrG VECTOR BUNDLES

  • Kawakami, Tomohiro
    • Communications of the Korean Mathematical Society
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    • v.23 no.2
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    • pp.257-268
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    • 2008
  • Let G and K be compact subgroups of orthogonal groups and $0{\leq}r<x<{\infty}$. We prove that every topological fiber bundle over a definable $C^r$ manifold whose structure group is K admits a unique strongly definable $C^r$ fiber bundle structure up to definable $C^r$ fiber bundle isomorphism. We prove that every G vector bundle over an affine definable $C^rG$ manifold admits a unique strongly definable $C^rG$ vector bundle structure up to definable $C^rG$ vector bundle isomorphism.

CLASSIFICATION OF EQUIVARIANT VECTOR BUNDLES OVER REAL PROJECTIVE PLANE

  • Kim, Min Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.319-335
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    • 2011
  • We classify equivariant topoligical complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most) three points are sufficient to classify equivariant vector bundles over real projective plane except one case. To do it, we relate the problem to classification on two-sphere through the covering map because equivariant vector bundles over two-sphere have been already classified.

EQUIVARIANT VECTOR BUNDLES AND CLASSIFICATION OF NONEQUIVARIANT VECTOR ORBIBUNDLES

  • Kim, Min Kyu
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.3
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    • pp.569-581
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    • 2011
  • Let a finite group R act smoothly on a closed manifold M. We assume that R acts freely on M except a union of closed submanifolds with codimension at least two. Then, we show that there exists an isomorphism between equivariant topological complex vector bundles over M and nonequivariant topological complex vector orbibundles over the orbifold M/R. By using this, we can classify nonequivariant vector orbibundles over the orbifold especially when the manifold is two-sphere because we have classified equivariant topological complex vector bundles over two sphere under a compact Lie group (not necessarily effective) action in [6]. This classification of orbibundles conversely explains for one of two exceptional cases of [6].

Cohomology of flat vector bundles

  • Kim, Hong-Jong
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.391-405
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    • 1996
  • In this article, we calculate the cohomology groups of flat vector bundles on some manifolds.

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Equivariant vector bundle structures on real line bundles

  • Shu, Dong-Youp
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.259-263
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    • 1996
  • Let G be a topological group and X a G space. For a given nonequivariant vector bundle over X there does not always exist a G equivariant vector bundle structure. In this paper we find some sufficient conditions for nonequivariant real line bundles to have G equivariant vector bundle structures.

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EQUIVARIANT VECTOR BUNDLES OVER GRAPHS

  • Kim, Min Kyu
    • Journal of the Korean Mathematical Society
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    • v.54 no.1
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    • pp.227-248
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    • 2017
  • In this paper, we reduce the classification problem of equivariant (topological complex) vector bundles over a simple graph to the classification problem of their isotropy representations at vertices and midpoints of edges. Then, we solve the reduced problem in the case when the simple graph is homeomorphic to a circle. So, the paper could be considered as a generalization of [3].