Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T04:46:12.937Z Has data issue: false hasContentIssue false
  • English
  • Français

On Steenrod Bundles and the van Kampen Theorem

Published online by Cambridge University Press:  20 November 2018

Vagn Lundsgaard Hansen
Vagn Lundsgaard Hansen*
Affiliation:
Mathematical Institute, The Technical University of Denmark Building303, DK-2800 Lyngby, Denmark
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a general method based on the van Kampen theorem for computing the fundamental group of the total space in certain Steenrod bundles. The method is applied to mapping spaces and Grassmann bundles.

Keywords

57M0555R99Fundamental groupSteenrod bundlevan Kampen's theoremmapping spaceGrassmann bundle
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 2 , 01 June 1988 , pp. 241 - 249
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Atiyah, M. F. and Jones, J. D. S., Topological aspects of Yang-Mills theory, Commun. Math. Phys. 61 (1978), pp. 97–118.Google Scholar
2. Hansen, V. L., On the space of maps of a closed surface into the 2-sphere, Math. Scand. 35 (1974), pp. 149–158.Google Scholar
3. Hansen, V. L., The homotopy groups of a space of maps between oriented closed surfaces, Bull. London Math. Soc. 15 (1983), pp. 360–364.Google Scholar
4. Hu, S. T., Concerning the homotopy groups of the components of the mapping space YSP Indagationes Math. 8 (1946), pp. 623–629.Google Scholar
5. Husemoller, D., Fibre bundles, 2nd ed., Graduate Texts in Math., Vol. 20. Springer-Verlag, Berlin-New York, 1966.Google Scholar
6. Massey, W. S., Algebraic topology: An introduction, Harcourt, Brace and World, New York, 1967.Google Scholar
7. Milnor, J. W., A procedure for killing the homotopy groups of differentiable manifolds, Symposia in Pure Math. A.M.S. Vol. III (1961), pp. 39–55.Google Scholar
8. Moller, J. M., On spaces of maps between complex projective spaces, Proc. Amer. Math. Soc. 91 (1984), pp. 471–476.Google Scholar
9. Steenrod, N. E., The topology of fibre bundles, Princeton Mathematical Series. Princeton Univ. Press, Princeton, N.J., 1951.Google Scholar
10. van Kampen, E. R., On the connection between the fundamental groups of some related spaces, Amer. J. Math. 55 (1933), pp. 261–267.Google Scholar
11. Whitehead, G. W., On the homotopy groups of spheres and rotation groups, Ann. of Math. 43 (1942), pp. 634–640.Google Scholar
12. Whitehead, G. W., Elements of homotopy theory, Graduate Texts in Math., Vol. 61, Springer-Verlag, Berlin-New York, 1978.Google Scholar