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

Lee, Chun-Nip

doi:10.1090/S0002-9947-1992-1031240-9

Stable splittings of the dual spectrum of the classifying space of a compact Lie group
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by Chun-Nip Lee

Trans. Amer. Math. Soc. 331 (1992), 77-111

DOI: https://doi.org/10.1090/S0002-9947-1992-1031240-9

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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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