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

Published online by Cambridge University Press:  20 November 2018

Stephen D. Theriault
Stephen D. Theriault*
Affiliation:
University of Virginia, Charlottesville, Virginia, 22904, U.S.A., e-mail: st7b@virginia.edu
*
Current address: University of Aberdeen Aberdeen, AB24 3UE, United Kingdom, email: s.theriault@maths.abdn.ac.uk
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Abstract

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James gave an integral homotopy decomposition of $\sum \Omega \sum X$, Hilton-Milnor one for $\Omega (\sum X\,\vee \,\sum Y)$, and Cohen-Wu gave $p$-local decompositions of $\Omega \sum X$ 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 $\text{co-}H$ spaces, and the Cohen-Wu decomposition has an analogue when the (double) suspension is replaced by a coassociative, cocommutative $\text{co-}H$ space.

Keywords

55P3555P45
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 1 , 01 February 2003 , pp. 181 - 203
Copyright
Copyright © Canadian Mathematical Society 2003

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