We give conditions for a map of spaces to induce maps of the homology decompositions of the spaces which are compatible with the homology sections and dual Postnikov invariants. Several applications of this result are obtained. We show how the homotopy type of the (n+1)st homology section depends on the homotopy type of the nth homology section and the (n+1)st homology group. We prove that all homology sections of a co-H-space are co-H-spaces, all n-equivalences of the homology decomposition are co-H-maps and, under certain restrictions, all dual Postnikov invariants are co-H-maps. We give a new proof of a result of Berstein and Hilton which gives conditions for a co-H-space to be a suspension.
@article{bwmeta1.element.bwnjournal-article-bcpv45i1p225bwm,
author = {Arkowitz, Martin},
title = {Induced mappings of homology decompositions},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {225-233},
zbl = {0941.55008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p225bwm}
}
Arkowitz, Martin. Induced mappings of homology decompositions. Banach Center Publications, Tome 43 (1998) pp. 225-233. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p225bwm/
[000] [Ar1] M. Arkowitz, The group of self-homotopy equivalences - A survey, Groups of Self-Homotopy Equivalences and Related Topics, Lecture Notes in Math. 1425, Springer-Verlag 1990, 170-203.
[001] [Ar2] M. Arkowitz, Co-H-spaces, Handbook of Algebraic Topology, Elsevier Science, North Holland, 1995, 1143-1173.
[002] [A-G] M. Arkowitz and M. Golasiński, Co-H-structures on Moore spaces of type (G,2), Can. J. of Math. 46 (1994), 673-686. | Zbl 0829.55006
[003] [A-M] M. Arkowitz and K. Maruyama, z Self homotopy equivalences which induce the identity on homology, cohomology or homotopy groups, Topology Appl. (to appear).
[004] [B-H1] I. Berstein and P. Hilton, Category and generalized Hopf invariants, Ill. J. of Math. 4 (1960), 437-451. | Zbl 0113.38301
[005] [B-H2] I. Berstein and P. Hilton, On suspensions and comultiplications, Topology 2 (1963), 73-82. | Zbl 0115.40403
[006] [B-C] E. Brown and A. Copeland, An homology analogue of Postnikov systems, Mich. Math. J. 6 (1959), 313-330. | Zbl 0093.37203
[007] [Cu1] C. Curjel, On the homology decomposition of polyhedra, Ill. J. of Math. 7 (1963), 121-136. | Zbl 0115.17002
[008] [Cu2] C. Curjel, A note on spaces of category ≤ 2, Math. Zeit. 80 (1963), 293-299. | Zbl 0105.17102
[009] [G-K] M. Golasiński and J. Klein, On maps into a co-H-space, (preprint).
[010] [Hi1] P. Hilton, Homotopy and Duality, Gordon and Breach, 1965.
[011] [Hi2] P. Hilton, On excision and principal fibrations, Comm. Math. Helv. 35 (1961), 77-84. | Zbl 0107.16804
[012] [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.
[013] [Wh] G. Whitehead, Elements of Homotopy Theory, Graduate Texts in Math. 61, Springer-Verlag (1978).