EQUIVARIANT VECTOR BUNDLES AND CLASSIFICATION OF NONEQUIVARIANT VECTOR ORBIBUNDLES

Let a ¯nite 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 com-plex vector bundles over M and nonequivariant topological com-plex vector orbibundles over the orbifold M=R: By using this, we can classify nonequivariant vector orbibundles over the orbifold es- when the manifold is two-sphere because we have classi¯ed equivariant topological complex vector bundles over two sphere un-der a compact Lie group (not necessarily e？？ective) action in [6]. This classi¯cation of orbibundles conversely explains for one of two exceptional cases of [6].