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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The $L_2$-localization of $W(\lowercase{n})$


Author: Robert D. Thompson
Journal: Trans. Amer. Math. Soc. 350 (1998), 1931-1944
MSC (1991): Primary 55P60; Secondary 55Q52, 55T15
MathSciNet review: 1467475
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Abstract: In this paper we analyze the localization of $W(n)$, the fiber of the double suspension map $S^{2n-1}\to \Omega^{2}S^{2n+1}$, with respect to $E(2)$. If four cells at the bottom of $D_pM^{2np-1}$, the $p$th extended power spectrum of the Moore spectrum, are collapsed to a point, then one obtains a spectrum $C$. Let $QM^{2np-1}\to QC$ be the James-Hopf map followed by the collapse map. Then we show that the secondary suspension map $BW(n)\to QM^{2np-1}$ has a lifting to the fiber of $QM^{2np-1}\to QC$ and this lifting is shown to be a $v_2$-periodic equivalence, hence an $E(2)$-equivalence.


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Additional Information

Robert D. Thompson
Affiliation: Hunter College and the Graduate Center, CUNY, 695 Park Avenue, New York, New York 10021
Email: thompson@math.hunter.cuny.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02149-7
PII: S 0002-9947(98)02149-7
Keywords: \protect{$L_2$}-localization, double suspension, \protect{$v_2$}-periodicity
Received by editor(s): July 23, 1996
Additional Notes: The author was partially supported by PSC-CUNY Grant 667399
Article copyright: © Copyright 1998 American Mathematical Society