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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A nonexistence result for Moore $ G$-spectra

Authors: S. R. Costenoble and S. Waner
Journal: Proc. Amer. Math. Soc. 113 (1991), 265-274
MSC: Primary 55N91; Secondary 55P47, 55P91
MathSciNet review: 1041013
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Abstract: In this paper we show that certain equivariant Moore spectra do not exist. Specifically, we give an example of a Bredon coefficient system for which there is no corresponding equivariant Moore CW-spectrum that is bounded below. This nonexistence result is stronger than nonexistence results shown previously; nonexistence of an equivariant Moore spectrum of type $ T$ implies, in particular, that there are no equivariant Moore spaces of type $ (T,n)$ for any $ n$. As a key step, we show that there is no strictly commutative Hopf space structure on the loop space $ Q{S^0}$ agreeing up to infinite loop homotopy with the usual addition.

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Keywords: Infinite loop maps, equivariant, Moore spectra, Moore spaces, coefficient system
Article copyright: © Copyright 1991 American Mathematical Society

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