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New proof of two Berstein-Hilton theorems

Author(s): Carmen Elvira; Jose L. Navarro
Journal: Proc. Amer. Math. Soc. 129 (2001), 3737-3740.
MSC (2000): Primary 55P40, 55P45; Secondary 55P30
Posted: July 10, 2001
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Abstract:

With arguments of Homotopy Theory and without the assumption of finite type, we give short proofs of two classic theorems which deal with the co--type of a suspension and the homotopy class of a suspension map.

References:

1.: I. Berstein and P. Hilton, On suspensions and comultiplications, Topology 2 (1963), 73-82 MR 27:762
2.: T. Ganea, A generalization of the homology and homotopy suspension, Comment. Math. Helv. 39 (1965), 295-322 MR 31:4033
3.: P. Hilton, On divisors and multiples of continuous maps, Fundamenta Math. 43 (1956), 358-386 MR 18:814b
4.: P. Hilton, Note on a theorem of Stasheff, Bull. Polish Acad. Sci. Math. 10 (1962), 127-131 MR 25:4536
5.: M. Walker, Homotopy pullbacks and applications to duality, Canad. J. Math. 29 (1977), 45-64 MR 55:11245

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Additional Information:

Carmen Elvira
Affiliation: Departamento de Analisis Economico, Universidad de Zaragoza, 50005-Zaragoza, Spain
Email: celvira@posta.unizar.es

Jose L. Navarro
Affiliation: Departamento de Matematicas, Universidad de Zaragoza, 50009-Zaragoza, Spain
Email: jlnava@posta.unizar.es

DOI: 10.1090/S0002-9939-01-06358-4
PII: S 0002-9939(01)06358-4
Keywords: Co-$H$-space, suspension, coprojective plane
Received by editor(s): March 20, 2000
Posted: July 10, 2001
Additional Notes: The first author was partially supported by DGS, project PD96-0740
Communicated by: Ralph L. Cohen
Copyright of article: Copyright 2001, American Mathematical Society


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