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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Brown-Peterson and ordinary cohomology theories of classifying spaces for compact Lie groups


Authors: Akira Kono and Nobuaki Yagita
Journal: Trans. Amer. Math. Soc. 339 (1993), 781-798
MSC: Primary 55N20; Secondary 55N22
DOI: https://doi.org/10.1090/S0002-9947-1993-1139493-4
MathSciNet review: 1139493
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Abstract: The Steenrod algebra structures of ${H^\ast }(BG;Z/p)$ for compact Lie groups are studied. Using these, Brown-Peterson cohomology and Morava $K$-theory are computed for many concrete cases. All these cases have properties similar as torsion free Lie groups or finite groups, e.g., $B{P^{odd}}(BG) = 0$.


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Keywords: Classifying space <IMG WIDTH="38" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$BG$">, compact Lie groups, <IMG WIDTH="38" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$BP$">-theory, cohomology operations
Article copyright: © Copyright 1993 American Mathematical Society