[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2011.24.3.17

EQUIVARIANT VECTOR BUNDLES AND CLASSIFICATION OF NONEQUIVARIANT VECTOR ORBIBUNDLES

Kim, Min Kyu (Department of Mathematics Education Gyeongin National University of Education)

Publication Information

Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 569-581 More about this Journal

Abstract

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].

Keywords

equivariant vector bundle; orbibundle;

Citations & Related Records

Reference

1	M. F. Atiyah, K-Theory, Addison-Wesley, 1989.
2	G. E. Bredon, Introduction to compact transformation groups, Academic Press, New York and London, 1972.
3	W. Chen, Y. Ruan, A new cohomology theory for orbifolds, Commun. Math. Phys. 248 (2004), 1-31. DOI
4	W. Chen, Y. Ruan, Orbifold quantum cohomology, arXiv:math/0005198v2
5	A. Constantin, B. Kolev, The theorem of Kerekjarto on periodic homeomorphisms of the disk and the sphere, Enseign. Math. (2) 40 (1994), 193-204.
6	M. K. Kim, Classification of equivariant vector bundles over two-sphere, submitted to Transform. Groups, arXiv:1005.0681v2.
7	M. K. Kim, Classification of equivariant vector bundles over real projective plane, J. Chungcheong Math. Soc. 24 (2011), no. 2, 319-335.
8	B. Kolev, Sous-groupes compacts d'homeomorphismes de la sphere, Enseign. Math. (2) 52 (2006), no. 3-4, 193-214.
9	I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 359-363. DOI ScienceOn
10	I. Satake, The Gauss-Bonnet Theorem for V -manifolds, J. Math. Soc. Japan 9 (1957), no. 4, 464-492. DOI
11	G. Segal, Equivariant K-theory, Inst. Hautes Etudes Sci. Publ. Math. 34 (1968), 129-151. DOI ScienceOn