Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-06-02T06:44:52.020Z Has data issue: false hasContentIssue false
  • English
  • Français

A Remark on Maps Between Classifying Spaces of Compact Lie Groups

Published online by Cambridge University Press:  20 November 2018

Zdzisław Wojtkowiak
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 show that two maps between classifying spaces of compact, connected Lie groups are homotopic after inverting the order of the Weyl group of the source if and only if they induce the same maps on rational cohomology. We shall also give some results on maps from classifying spaces of finite groups to classifying spaces of compact Lie groups. Among other things we construct a map from B(Z/2 + Z/2 4- Z/3) into BSO(3) which is not induced by a homomorphism.

Keywords

55P99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 4 , 01 December 1988 , pp. 452 - 458
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Bousfield, A. K., Kan, D. M., Homotopy limits, Completions and Localizations Lecture Notes in Math. 304, Springer, 1972.Google Scholar
2. Dwyer, W. and Zabrodsky, A., Maps between classifying spaces in Algebraic Topology Barcelona 1986, Lecture Notes in Math. 1298, Springer, 1987, pp. 106–119.Google Scholar
3. Wojtkowiak, Z., Maps from BIT into X Quart. J. Math. Oxford (2), 39 (1988), pp. 117–127.Google Scholar
4. Zabrodsky, A., Maps between classifying spaces, p-groups and tori unpublished.Google Scholar