• 대한수학회논문집
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• 제11권1호
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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.

• 자연과학논문집
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• 제10권1호
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• pp.13-16
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• 1998

원 위에서의 모든 복소 vector bundle은 line bundle로 나누어지며 첫째 Chern class는 복소 line bundle을 분류한다. 이것은 원위에서의 모든 복소 vector bundle은 trivial 하다는 것을 의미한다. 이 논문에서는 군작용이 있을 경우에는 원위에서의 복소 vector bundle중에 trivial하지 않는 bundle이 존재함을 보였다.

• 자연과학논문집
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• 제8권2호
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• pp.17-20
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• 1996

Fiber의 dimension이 일일 때, Equivariant Serre problem이 실 대수 범주에서 맞다는 것을 보였다. 즉 실 표현공간 위에서의 equivariant line bundle은 실 표현공간과 어떤 G-module의 product bundle과 동치임을 보였다.

• 자연과학논문집
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• 제11권1호
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• pp.11-14
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• 1999

군 G가 compact Lie군이며 $\rho$ : G $\rightarrow$ O(2)가 homomorphism일 때 군 G가 가환군이면 원위에서 실 G-vector bundle은 실 G-line bundle들의 Whitney 합이거나 G-plan bundle들의 Whitney 합과 isomorphic 하다는 것을 보였다.

• 충청수학회지
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• 제24권2호
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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.

• 대한수학회지
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• 제54권1호
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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].

• 충청수학회지
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• 제24권3호
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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].

• 대한수학회논문집
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• 제10권4호
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• pp.949-961
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• 1995

Let f be a smooth G map from a nonsingular real algebraic G variety to an equivariant Grassmann variety. We use some G vector bundle theory to find a necessary and sufficient condition to approximate f by an entire rational G map. As an application we algebraically approximate a smooth G map between G spheres when G is an abelian group.

• 대한수학회지
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• 제39권3호
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• pp.331-349
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• 2002

Let G be a reductive algebraic group and let B, F be G-modules. We denote by $VEC_{G}$ (B, F) the set of isomorphism classes in algebraic G-vector bundles over B with F as the fiber over the origin of B. Schwarz (or Karft-Schwarz) shows that $VEC_{G}$ (B, F) admits an abelian group structure when dim B∥G = 1. In this paper, we introduce a stable functor $VEC_{G}$ (B, $F^{\chi}$) and prove that it is an abelian group for any G-module B. We also show that this stable functor will have nice properties.