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

 

Classifying spaces and homotopy
sets of axes of pairings


Author: Kenshi Ishiguro
Journal: Proc. Amer. Math. Soc. 124 (1996), 3897-3903
MSC (1991): Primary 55R35; Secondary 55P15, 55P60
MathSciNet review: 1343701
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Abstract: We consider the maps between classifying spaces of the form $BK \times BL \rightarrow BG$. The main theorem shows that if the restriction map on $BL$ is a weak epimorphism, then the restriction on $BK$ should factor through the classifying spaces of the center of the compact Lie group $G$. An application implies that $BG$ is an H-space (Hopf space) if and only if $G$ is abelian.


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Additional Information

Kenshi Ishiguro
Affiliation: Department of Mathematics, Fukuoka University, Fukuoka 814-80, Japan

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03497-1
PII: S 0002-9939(96)03497-1
Keywords: Classifying space, mapping spaces, $p$-completion, Lie groups, weak epimorphism, pairing
Received by editor(s): April 10, 1995
Received by editor(s) in revised form: June 15, 1995
Dedicated: Dedicated to Professor Teiichi Kobayashi on his 60th birthday
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society