Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T06:13:10.346Z Has data issue: false hasContentIssue false
  • English
  • Français

Pull-Backs in Homotopy Theory

Published online by Cambridge University Press:  20 November 2018

Michael Mather
Michael Mather*
Affiliation:
University of Toronto, Toronto, Ontario-, and University of Otago, Dunedin, New Zealand
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.

The (based) homotopy category consists of (based) topological spaces and (based) homotopy classes of maps. In these categories, pull-backs and push-outs do not generally exist. For example, no essential map between Eilenberg-MacLane spaces of different dimensions has a kernel. In this paper we define homotopy pull-backs and push-outs, which do exist and which behave like pull-backs and push-outs, and we give some of their properties. Applications may be found in [3; 5; 6 and 14].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 225 - 263
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Dold, A., Partitions of unity in the theory of fibrations, Ann. of Math. 78 (1963), 223–255.Google Scholar
2. Epstein, D. B. A., A group with zero homology, Proc. Cambridge Phil. Soc. 64 (1968), 599–601.Google Scholar
3. Fantham, P. H. H. and Mather, M., On James's construction, Typescript.Google Scholar
4. Ganea, T., A generalisation of the homology and homotopy suspension, Comment. Math. Helv. 39 (1965), 295–322.Google Scholar
5. Mather, M., Hurewicz theorems for pairs and squares, Math. Scand. 32 (1973), 269–272.Google Scholar
6. Mather, M., A generalisation of Ganea s theorem on the mapping cone of the inclusion of a fibre, J. London Math. Soc. (2), J J (1975), 121–122.Google Scholar
7. Milnor, J., On spaces having the homotopy type of CW-complexes, Trans. Amer. Math. Soc. 90 (1959), 272–280.Google Scholar
8. Nomura, Y., On extensions of triads, Nagoya Math. J. 27 (1966), 249–277.Google Scholar
9. Nomura, Y., The Whitney join and its dual, Osaka J. Math. 7(1970), 353–373.Google Scholar
10. Spanier, E. H., Algebraic topology (McGraw-Hill, 1966).Google Scholar
11. Svarc, A. S., On the genus of a fibred space, Dokl. Akad. Nauk. SSSR. 126 (1959), 719–722. (Russian)Google Scholar
12. Vogt, R. M., A note on homotopy equivalences, Proc. Amer. Math. Soc. 32 (1972), 627–629.Google Scholar
13. Vogt, R. M., Homotopy limits and colimits, Math. Z. 131,. (1973), 11–52.Google Scholar
14. Walker, M., Duality in homotopy theory, Ph.D. thesis, University of Toronto, 1972.Google Scholar