Abstract
Let K(n)* (–) be the n-th Morava K-theory at 2. We discuss the existence in K(n)* (Bℤ/2 × Bℤ/2) of a basis whose elements are just permuted by the canonical action of GL 2(\({\Bbb F}\) 2) ≅ Aut(ℤ/2 × ℤ/2). We exhibit such a basis when n = 3 and prove that it does not exist when n = 2.
AMS 1991 Subject Classification 55N20, 55N22.
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References
M. Brunetti, ‘A family of 2(p - l)-sparse cohomology theories and some actions on h*(BC p n)’, to appear on Math. Proc. Camb. Phil. Soc.
M. Lazard, ‘Lois de groupes et analyseurs’, Ann. Sci. Ecole Norm. Sup.72 (1955), 299–400.
U. Würgler, ‘Commutative ring-spectra of characteristic 2’, Comment. Math. Helυ.61 (1986), 33–45.
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© 1996 Birkhäuser Verlag
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Brunetti, M. (1996). On the canonical GL 2(\({\Bbb F}\) 2)-module structure of K(n)*(Bℤ/2 × Bℤ/2). In: Broto, C., Casacuberta, C., Mislin, G. (eds) Algebraic Topology: New Trends in Localization and Periodicity. Progress in Mathematics, vol 136. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9018-2_4
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DOI: https://doi.org/10.1007/978-3-0348-9018-2_4
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9869-0
Online ISBN: 978-3-0348-9018-2
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