Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T02:23:18.311Z Has data issue: false hasContentIssue false
  • English
  • Français

On the integral cohomology of the seven-connective cover of BO

Published online by Cambridge University Press:  17 April 2009

Tze Beng Ng
Tze Beng Ng
Affiliation:
Department of Mathematics, National University of Singapore, Singapore
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.

Let BO, BSO and BSpin be the classifying spaces for the infinite orthogonal, infinite special orthogonal and infinite spinor groups respectively. It is well known that their integral cohomology rings have torsion only of order 2. In this paper we present an elementary proof that for the 7-connective cover of BO, BO〈8〉, the integral cohomology ring H* (BO〈8〉; Z) too has torsion only of order 2. The method follows that of Borel and Hirzebruch and a result of Wu concerning the Steenrod reduced mod p operation for an odd prime p on the Pontrjagin classes.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 1 , August 1988 , pp. 11 - 17
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Borel, A. and Hirzebruch, F., ‘Characteristic classes and homogeneous spaces II’, Amer. J. Math. 81 (1959), 315–382.CrossRefGoogle Scholar
[2]Borel, A., Lecture Notes in Mathematics 36, in (Springer Verlag, 1967).Google Scholar
[3]Cartan, H., ‘Sur les groupes d'Eilenberg-MacLane H(π, n), I, II,’, Proc. Nat. Acad. Sci., U.S.A. vol 40 (1954), 467–471, 704–707:CrossRefGoogle Scholar
[4]Ng, Tze-Beng, ‘A note on the mod 2 cohomology of BŜOn < 16 >’, Canad. J. Math. 37 (1985), 893–907.CrossRefGoogle Scholar
[5]Thomas, E., ‘On the cohomology groups of the classifying space for the stable spinor group’, Bol. Soc. Mat. Mericana 7 (1962), 57–69.Google Scholar
[6]Wu, W.T., ‘On Pontrjagin classes II’, Acta. Math. Sinica 4 (1954), 171–199.Google Scholar