Equivariant Real Vector Bundles over a Circle

원위에서의 Equivariant Real Vector Bundles

Let G be a compact Lie group and let $\rho$ : G $\rightarrow O(2) be a homomorphism. Denote by V the G-module associated with $\rho$ and by S(V) the unit circle of V. In this paper, we show that if G is abelian, then a real G-vector bundle over S(V) is isomorphic to Whitney sum of real G-line or G-plane bundles.

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.