Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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EQUIVARIANT VECTOR BUNDLES AND CLASSIFICATION OF NONEQUIVARIANT VECTOR ORBIBUNDLES

  • Kim, Min Kyu (Department of Mathematics Education Gyeongin National University of Education)
  • Received : 2011.07.04
  • Accepted : 2011.08.13
  • Published : 2011.09.30
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Abstract

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].

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References

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