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# A Case When the Fiber of the Double Suspension is the Double Loops on Anick's Space

Published:2010-07-26
Printed: Dec 2010
• Stephen D. Theriault,
Department of Mathematical Sciences, University of Aberdeen, Aberdeen, United Kingdom
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## Abstract

The fiber $W_{n}$ of the double suspension $S^{2n-1}\rightarrow\Omega^{2} S^{2n+1}$ is known to have a classifying space $BW_{n}$. An important conjecture linking the $EHP$ sequence to the homotopy theory of Moore spaces is that $BW_{n}\simeq\Omega T^{2np+1}(p)$, where $T^{2np+1}(p)$ is Anick's space. This is known if $n=1$. We prove the $n=p$ case and establish some related properties.
 Keywords: double suspension, Anick's space
 MSC Classifications: 55P35 - Loop spaces 55P10 - Homotopy equivalences

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