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1998 | 45 | 1 | 225-233
Tytuł artykułu

Induced mappings of homology decompositions

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Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
45
Numer
1
Strony
225-233
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Mathematics Department, Dartmouth College, Hanover, New Hampshire 03755, U.S.A.
Bibliografia
  • [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.
  • [Ar2] M. Arkowitz, Co-H-spaces, Handbook of Algebraic Topology, Elsevier Science, North Holland, 1995, 1143-1173.
  • [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.
  • [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).
  • [B-H1] I. Berstein and P. Hilton, Category and generalized Hopf invariants, Ill. J. of Math. 4 (1960), 437-451.
  • [B-H2] I. Berstein and P. Hilton, On suspensions and comultiplications, Topology 2 (1963), 73-82.
  • [B-C] E. Brown and A. Copeland, An homology analogue of Postnikov systems, Mich. Math. J. 6 (1959), 313-330.
  • [Cu1] C. Curjel, On the homology decomposition of polyhedra, Ill. J. of Math. 7 (1963), 121-136.
  • [Cu2] C. Curjel, A note on spaces of category ≤ 2, Math. Zeit. 80 (1963), 293-299.
  • [G-K] M. Golasiński and J. Klein, On maps into a co-H-space, (preprint).
  • [Hi1] P. Hilton, Homotopy and Duality, Gordon and Breach, 1965.
  • [Hi2] P. Hilton, On excision and principal fibrations, Comm. Math. Helv. 35 (1961), 77-84.
  • [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, 1966.
  • [Wh] G. Whitehead, Elements of Homotopy Theory, Graduate Texts in Math. 61, Springer-Verlag (1978).
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv45i1p225bwm
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