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THE CONE LENGTH OF A PRODUCT OF CO-H-SPACES AND A PROBLEM OF GANEA

Published online by Cambridge University Press:  28 November 2001

MARTIN ARKOWITZ  and
DONALD STANLEY
MARTIN ARKOWITZ
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA; Martin.Arkowitz@dartmouth.edu
DONALD STANLEY
Affiliation:
Department of Mathematical Science, University of Alberta, Edmonton, AB, Canada T6G 2G1, stanley@math.ualberta.ca
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Abstract

It is proved that the cone length or strong category of a product of two co-H-spaces is less than or equal to two. This yields the following positive solution to a problem of Ganea. Let α ∈ π2p(S3) be an element of order p, p a prime [ges ] 3, and let X(p) = S3∪αe2p+1. Then X(p) × X(p) is the mapping cone of some map φ : Y → Z where Z is a suspension.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 6 , November 2001 , pp. 735 - 742
Copyright
© The London Mathematical Society 2001

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