Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-18T03:44:25.600Z Has data issue: false hasContentIssue false
  • English
  • Français

MOD-C Postnikov Approximation of a 1-Connected Space

Published online by Cambridge University Press:  20 November 2018

A. Behera  and
S. Nanda
A. Behera
Affiliation:
University of Toronto, Toronto, Ontario
S. Nanda
Affiliation:
Regional Engineering College, Rourkela, India
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context [4]. They have also shown that if the set of morphisms is saturated then the Adams completion of an object is characterized by a certain couniversai property. We want to prove a stronger version of this result by dropping the saturation assumption on the set of morphisms; we also prove that the canonical map from an object to its Adams completion is an element of the set of morphisms under very moderate assumptions. These two results are fairly general in nature and are applicable to most cases of interest. Further using these two results and introducing “modulo a Serre class C of abelian groups” [9] we have obtained the mod-C Postnikov approximation of a 1-connected based CW-complex, with the help of a suitable set of morphisms.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 3 , 01 June 1987 , pp. 527 - 543
Copyright
Copyright © Canadian Mathematical Society 1987

References

1. Adams, J. F., Localization and completion, Lecture Notes in Mathematics, University of Chicago (1975).Google Scholar
2. Adams, J. F., Idempotent functors in homotopy theory in Manifolds (University of Tokyo Press, Tokyo 1973), 247–253.Google Scholar
3. Bucur, I. and Deleanu, A., Introduction to the theory of categories functors (Wiley Interscience Publication, 1968).Google Scholar
4. Deleanu, A., Frei, A. and Hilton, P. J., Generalized Adams completion, Cahiers de Top et Geom. Diff. 75 (1972), 61–82.Google Scholar
5. Deleanu, A., Existence of the Adams completion for CW-complexes, J. Pure and App. Alg. 4 (1974), 299–308.Google Scholar
6. Deleanu, A., Existence of the Adams completion for objects of cocomplete categories, J. Pure and App. Alg. 6 (1975), 31–39.Google Scholar
7. Nanda, S., Adams completion and Postnikov systems, Colloq. Math. 40 (1978), 99–110.Google Scholar
8. Nanda, S., Adams completion and its applications, Queen's Papers in Pure and App. Math. 57 (1979).Google Scholar
9. Spanier, E. H., Algebraic topology (McGraw-Hill, 1966).Google Scholar
10. Switzer, R. M., Algebraic topology — homotopy and homology (Springer, Berlin, 1975).CrossRefGoogle Scholar