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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
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Abstract

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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

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