Title:"The cone length of a product of co-H-spaces and
a problem of Ganea"
Authors: Martin Arkowitz and Donald Stanley
Mathematics Subject Classification: Primary 55M30, 55P50.
Secondary 55P45.
Address:
Martin Arkowitz
Department of Mathematics
Dartmouth College
Hanover
NH 03755
USA
Don Stanley
Department of Mathematical Sciences
University of Alberta
Edmonton, Alberta
T6G 2G1
Canada
email: Martin.Arkowitz@dartmouth.edu stanley@math.ualberta.ca
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 $\alpha \in \pi_{2p}(S^3)$ be an element of order p, p
a prime $\geq 3$, and let $X(p)=S^3\cup_{\alpha}e^{2p+1}$.
Then $X(p)\times X(p)$ is the mapping cone of some map
$\phi:Y \rightarrow Z$, where $Z$ is a suspension.