The $L_2$-localization of $W(n)$

In this paper we analyze the localization of W (n), the ber of the double suspension map S2n 1 ! 2S2n+1, with respect to E(2). If four cells at the bottom of DpM2np 1 ,t he pth extended power spectrum of the Moore spectrum, are collapsed to a point, then one obtains a spectrum C.L et QM2np 1 ! QC be the James-Hopf map followed by the collapse map. Then we show that the secondary suspension map BW(n) ! QM2np 1 has a lifting to the ber of QM2np 1 ! QC and this lifting is shown to be a v2-periodic equivalence, hence an E(2)-equivalence.