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Functorial Decompositions of Looped Coassociative Co-H Spaces

Published online by Cambridge University Press:  20 November 2018

P. Selick ,
S. Theriault  and
J. Wu
P. Selick
Affiliation:
Deparment of Mathematics, University of Toronto, Toronto, ON, M5S 2E4 e-mail: selick@math.toronto.edu
S. Theriault
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, Aberdeen AB24 3UE, U.K. e-mail: s.theriault@maths.abdn.ac.uk
J. Wu
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 117543 e-mail: matwuj@nus.edu.sg
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Abstract

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Selick and Wu gave a functorial decomposition of $\Omega \Sigma X$ for path-connected, $p$-local $CW$-complexes $X$ which obtained the smallest nontrivial functorial retract ${{A}^{\min }}\left( X \right)$ of $\Omega \Sigma X$. This paper uses methods developed by the second author in order to extend such functorial decompositions to the loops on coassociative co-$H$ spaces.

Keywords

55P53Homotopy decompositioncoassociative co-H spaces
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 4 , 01 August 2006 , pp. 877 - 896
Copyright
Copyright © Canadian Mathematical Society 2006

References

[BH] Berstein, I. and Harper, J. R., Cogroups which are not suspensions. In: Algebraic Topology, Lecture Notes in Math. 1370, 1989, pp. 63–86.Google Scholar
[BK] Bousfield, A. K. and Kan, D. M., Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics 304, Springer-Verlag, Berlin, 1972.Google Scholar
[G] Ganea, T., Cogroups and suspensions. Invent.Math. 9(1970), 185–197.Google Scholar
[M] May, J. P., A Concise Course in Algebraic Topology. Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1999.Google Scholar
[SW1] Selick, P. and Wu, J., On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions. Mem. Amer. Math. Soc. 148, No. 701, 2000.Google Scholar
[SW2] Selick, P. and Wu, J., The functor Amin on p-local spaces. Math. Z., to appear.Google Scholar
[SW3] Selick, P. and Wu, J., On functorial decompositions of self-smash products. Manuscripta Math. 111(2003), no. 4, 435–457.Google Scholar
[T] Theriault, S. D., Homotopy decompositions involving the loops of coassociative co-H spaces. Canad. J. Math. 55(2003), no. 1, 181–203.Google Scholar