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Homotopy Decompositions Involving the Loops of Coassociative Co-$H$ Spaces

Open Access article
 Printed: Feb 2003
  • Stephen D. Theriault
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James gave an integral homotopy decomposition of $\Sigma\Omega\Sigma X$, Hilton-Milnor one for $\Omega (\Sigma X\vee\Sigma Y)$, and Cohen-Wu gave $p$-local decompositions of $\Omega\Sigma X$ if $X$ is a suspension. All are natural. Using idempotents and telescopes we show that the James and Hilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-$H$ spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative co-$H$ space.
MSC Classifications: 55P35, 55P45 show english descriptions Loop spaces
$H$-spaces and duals
55P35 - Loop spaces
55P45 - $H$-spaces and duals

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