• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.649-654
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• 1999

We consider the forgetful map from the group of equivariant self equivalences to the group of non-equivariant self equivalences. A sufficient condition for this forgetful map being a monomorphism is obtained. Several examples are given.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.111-137
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• 2021

Higson proved that every homotopy invariant, stable and split exact functor from the category of C⁎-algebras to an additive category factors through Kasparov's KK-theory. By adapting a group equivariant generalization of this result by Thomsen, we generalize Higson's result to the inverse semigroup and locally compact, not necessarily Hausdorff groupoid equivariant setting.

• 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.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.371-386
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• 1998

Let G be a compact Lie group and M a semialgebraic G space in some orthogonal representation space of G. We prove that if G is finite then M has an equivariant semialgebraic triangulation. Moreover this triangulation is unique. When G is not finite we show that M has a semialgebraic G CW complex structure, and this structure is unique. As a consequence compact semialgebraic G space has an equivariant simple homotopy type.