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

Published online by Cambridge University Press:  20 November 2018

Stephen D. Theriault
Stephen D. Theriault*
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen, United Kingdom e-mail: s.theriault@maths.abdn.ac.uk
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Abstract

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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.

Keywords

55P3555P10double suspensionAnick's space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 53 , Issue 4 , 01 December 2010 , pp. 730 - 736
Copyright
Copyright © Canadian Mathematical Society 2010

References

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