EQUIVARIANT VECTOR BUNDLES AND CLASSIFICATION OF NONEQUIVARIANT VECTOR ORBIBUNDLES

• 발행기관: 충청수학회
• 저자명: Min Kyu Kim
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 24, No. 3, 569~581쪽, 전체 13쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2011.08.30

영문 초록

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].

목차

1. Introduction

2. Pullback of vector orbibundle

3. Line orbibundles over M=R

4. Orbibundles over S2=R