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Proceedings of the American Mathematical Society

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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

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