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ISSN 1088-6850(e) ISSN 0002-9947(p)

Real connective K-theory and the quaternion group

Author(s): Dilip Bayen; Robert R. Bruner
Journal: Trans. Amer. Math. Soc. 348 (1996), 2201-2216.
MSC (1991): Primary 19L41, 19L47, 19L64, 55N15, 55R35, 55Q91, 55M05
MathSciNet review: 1329527
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Abstract: Let $ko$ be the real connective K-theory spectrum. We compute $ko_*BG$ and $ko^*BG$ for groups $G$ whose Sylow 2-subgroup is quaternion of order 8. Using this we compute the coefficients $t(ko)^G_*$ of the $G$ fixed points of the Tate spectrum $t(ko)$ for $G = Sl_2(3)$ and $G = Q_8$ . The results provide a counterexample to the optimistic conjecture of Greenlees and May [9, Conj. 13.4], by showing, in particular, that $t(ko)^G$ is not a wedge of Eilenberg-Mac Lane spectra, as occurs for groups of prime order.

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