Title of Paper:
Homology of the universal covering of a co-H-space
Authors:
Norio Iwase, Shiroshi Saito and Toshio Sumi
AMS Classification numbers:
Primary 55P45, Secondary 19A13
Addresses of Authors:
(N.Iwase) Graduate School of Mathematics,
Kyushu University, Fukuoka, Japan.
(S.Saito) Department of Mathematics,
Shinshu University, Matsumoto, Japan.
(T.Sumi) Department of Art and Information Design,
Kyushu Institute of Design, Fukuoka, Japan.
Email addresses of Authors:
(N.Iwase) n.iwase@maths.abdn.ac.uk
(T.Sumi) sumi@kyushu-id.ac.jp
Included EPS or PS files:
coh-fig1.eps, coh-fig2.eps and coh-fig3.eps
Text of Abstract:
The problem 10 posed by Tudor Ganea is known as the Ganea
conjecture on a co-H-space, dual notion to a Hopf space.
We show a homological property of co-H-spaces in a slightly
general situation. As its corollary, the conjecture is verified
for co-H-spaces of finite type with homology groups concentrated
in dimensions 1 and $*$, $n+1 \leq * \leq n+2$, for some $n \geq 1$.
Also, such a co-H-space has the homotopy type of a wedge sum of
circles, Moore speces of type $(A,n+1)$ and $(B,n+2)$, for some
finitely generated abelian groups $A$ and $B$.