Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

CLASSIFICATION OF EQUIVARIANT VECTOR BUNDLES OVER REAL PROJECTIVE PLANE

  • Kim, Min Kyu (Department of Mathematics Education, Gyeongin National University of Education)
  • Received : 2011.03.19
  • Accepted : 2011.05.16
  • Published : 2011.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

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.

Keywords

References

  1. G. E. Bredon, Introduction to compact transformation proups, Academic Press, New York and London, 1972.
  2. J.-H. Cho, S. S. Kim, M. Masuda, D. Y. Suh, Classification of equivariant complex vector bundles over a circle, J. Math. Kyoto Univ. 41 (2001), 517-534. https://doi.org/10.1215/kjm/1250517616
  3. A. Constantin, B. Kolev, The theorem of Kerekjarto on periodic homeomorphisms of the disk and the sphere, Enseign. Math. (2) 40 (1994), 193-204.
  4. M. K. Kim, Classification of equivariant vector bundles over two-sphere, arXiv:1005.0681v2.
  5. B. Kolev, Sous-groupes compacts d'homeomorphismes de la sphere, Enseign. Math. (2) 52 (2006), no. 3-4, 193-214.
  6. E. G. Rees, Notes on geometry, Universitext, Springer-Verlag, Berlin-New York, 1983.
  7. G. Segal, Equivariant K-theory, Inst. Hautes Etudes Sci. Publ. Math. 34 (1968), 129-151. https://doi.org/10.1007/BF02684593