Journal of Mathematics of Kyoto University
- J. Math. Kyoto Univ.
- Volume 39, Number 2 (1999), 277-286.
The cohomology of $BO (n)$ with twisted integer coefficients
Abstract
Let $H^{*}(BO(n), \mathbf{Z}^{t})$ be the graded cohomology group of the classifying space $BO(n)$ with twisted integer coefficients. Then $H^{*}(BO(n); \mathbf{Z}) \bigoplus H^{*}(BO(n); \mathbf{Z}^{t})$ has a structure of a $\mathbf{Z} \bigoplus \mathbf{Z}_{2}$ graded ring. In the paper this ring is described in terms of generators and relations. It extends the results on the integer cohomology ring $H^{*}(BO(n); \mathbf{Z})$ derived in [B] and [F].
Article information
Source
J. Math. Kyoto Univ., Volume 39, Number 2 (1999), 277-286.
Dates
First available in Project Euclid: 17 August 2009
Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250517912
Digital Object Identifier
doi:10.1215/kjm/1250517912
Mathematical Reviews number (MathSciNet)
MR1709293
Zentralblatt MATH identifier
0946.55009
Subjects
Primary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]
Secondary: 57R20: Characteristic classes and numbers
Citation
Čadek, Martin. The cohomology of $BO (n)$ with twisted integer coefficients. J. Math. Kyoto Univ. 39 (1999), no. 2, 277--286. doi:10.1215/kjm/1250517912. https://projecteuclid.org/euclid.kjm/1250517912
