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

 

Mapping spaces of compact Lie groups and $ p$-adic completion


Authors: David Blanc and Dietrich Notbohm
Journal: Proc. Amer. Math. Soc. 117 (1993), 251-258
MSC: Primary 55R35; Secondary 55P60
MathSciNet review: 1112487
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Abstract: If $ {\mathbf{BG}},\;{\mathbf{BH}}$ are the classifying spaces of compact Lie groups, with $ {\mathbf{H}}$ connected, then the mapping space functor $ {\mathbf{map}}({\mathbf{BG}}, - )$ commutes with $ p$-completion on $ {\mathbf{BH}}$: i.e., for each $ f:{\mathbf{BG}} \to {\mathbf{BH}}$ the component $ ({\mathbf{map}}{({\mathbf{BG}},{\mathbf{BH}})_f})_p^ \wedge $ is $ p$-complete, and is homotopy equivalent to $ {\mathbf{map}}{({\mathbf{BG}},{\mathbf{BH}}_p^ \wedge )_{i \circ f}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1112487-6
PII: S 0002-9939(1993)1112487-6
Keywords: Mapping space, Lie group, completion
Article copyright: © Copyright 1993 American Mathematical Society