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A Case When the Fiber of the Double Suspension is the Double Loops on Anick's Space
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- Journal:
- Canadian Mathematical Bulletin / Volume 53 / Issue 4 / 01 December 2010
- Published online by Cambridge University Press:
- 20 November 2018, pp. 730-736
- Print publication:
- 01 December 2010
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- Article
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The fiber
${{W}_{n}}$ of the double suspension 
${{S}^{2n-1}}\,\to \,{{\Omega }^{2}}{{S}^{2n+1}}$ is known to have a classifying space 
$B{{W}_{n}}$. An important conjecture linking the 
$EPH$ sequence to the homotopy theory of Moore spaces is that 
$B{{W}_{n}}\,\simeq \,\Omega {{T}^{2np+1}}(p)$, 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.
