Real connective K-theory and

the quaternion group

Authors:
Dilip Bayen and Robert R. Bruner

Journal:
Trans. Amer. Math. Soc. **348** (1996), 2201-2216

MSC (1991):
Primary 19L41, 19L47, 19L64, 55N15, 55R35, 55Q91, 55M05

DOI:
https://doi.org/10.1090/S0002-9947-96-01516-4

MathSciNet review:
1329527

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the real connective K-theory spectrum. We compute and for groups whose Sylow 2-subgroup is quaternion of order 8. Using this we compute the coefficients of the fixed points of the Tate spectrum for and . The results provide a counterexample to the optimistic conjecture of Greenlees and May [9, Conj. 13.4], by showing, in particular, that is not a wedge of Eilenberg-Mac Lane spectra, as occurs for groups of prime order.

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Additional Information

**Dilip Bayen**

Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Email:
dbayen@math.wayne.edu

**Robert R. Bruner**

Affiliation:
Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Email:
rrb@math.wayne.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01516-4

Keywords:
Quaternion group,
classifying space,
connective K-theory,
Tate cohomology

Received by editor(s):
August 10, 1994

Article copyright:
© Copyright 1996
American Mathematical Society