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Stable splittings of the dual spectrum of the classifying space of a compact Lie group


Author: Chun-Nip Lee
Journal: Trans. Amer. Math. Soc. 331 (1992), 77-111
MSC: Primary 55P42; Secondary 55Q45
DOI: https://doi.org/10.1090/S0002-9947-1992-1031240-9
MathSciNet review: 1031240
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Abstract: For a compact Lie group $ G$, there is a map from the $ G$-equivariant fixed point spectrum of the zero sphere to the dual spectrum of the classifying space of $ G, DB{G_ + }$. When $ G$ is finite, the affirmative solution to Segal's conjecture states that this map is an equivalence upon appropriate completion of the source. In the case of a compact Lie group, we obtain splitting results of $ DB{G_ + }$ via this map upon taking $ p$-adic completions.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1031240-9
Article copyright: © Copyright 1992 American Mathematical Society

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