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

[摘要] James gave an integral homotopy decomposition of $SigmaOmegaSigma X$, Hilton-Milnor one for $Omega (Sigma XveeSigma Y)$, and Cohen-Wu gave$p$-local decompositions of $OmegaSigma X$ if $X$ is a suspension. Allare natural. Using idempotents and telescopes we show that the James andHilton-Milnor decompositions have analogues when the suspensions are replaced by coassociative co-$H$ spaces, and the Cohen-Wu decompositionhas an analogue when the (double) suspension is replaced by a coassociative,cocommutative co-$H$ space.

[学科分类] 数学（综合）