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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The mod 2 cohomology of the linear groups
over the ring of integers


Authors: Dominique Arlettaz, Mamoru Mimura, Koji Nakahata and Nobuaki Yagita
Journal: Proc. Amer. Math. Soc. 127 (1999), 2199-2212
MSC (1991): Primary 20G10; Secondary 19D55, 20J05, 55R40, 55S10
Published electronically: April 8, 1999
MathSciNet review: 1646320
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper completely determines the Hopf algebra structure of the mod 2 cohomology of the linear groups $GL(\mathbb{Z})$, $SL(\mathbb{Z})$ and $St(\mathbb{Z})$ as a module over the Steenrod algebra, and provides an explicit description of the generators.


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Additional Information

Dominique Arlettaz
Affiliation: Institut de Mathématiques, Université de Lausanne, 1015 Lausanne, Switzerland
Email: dominique.arlettaz@ima.unil.ch

Mamoru Mimura
Affiliation: Department of Mathematics, Faculty of Science, Okayama University, Okayama, Japan 700
Email: mimura@math.okayama-u.ac.jp

Koji Nakahata
Affiliation: Institut de Mathématiques, Université de Lausanne, 1015 Lausanne, Switzerland
Email: koji.nakahata@ima.unil.ch

Nobuaki Yagita
Affiliation: Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan
Email: yagita@mito.ipc.ibaraki.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05183-7
PII: S 0002-9939(99)05183-7
Received by editor(s): September 15, 1997
Published electronically: April 8, 1999
Additional Notes: We would like to thank Christian Ausoni for his helpful comments on Bökstedt’s work \cite{Bok} and the referee for his interesting suggestions. The third author thanks the Swiss National Science Foundation for financial support.
Communicated by: Ralph Cohen
Article copyright: © Copyright 1999 American Mathematical Society