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

http://dx.doi.org/10.4153/CMB-2010-079-9
Canad. Math. Bull. 53(2010), 730-736

  Published:2010-07-26
 Printed: Dec 2010

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.