Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T13:43:06.926Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite Complexes Whose Self-Homotopy Equivalence Groups Realize the Infinite Cyclic Group

Published online by Cambridge University Press:  20 November 2018

Ken-Ichi Maruyama
Ken-Ichi Maruyama*
Affiliation:
Department of Mathematics, Faculty of Education Chiba University Yayoicho, Chiba Japan e-mail:, maruyama@cue.e.chiba-u.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

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.

Examples of finite complexes are given whose self-homotopy equivalences group is isomorphic to the group of integers.

Keywords

55P10Self-homotopy equivalencerealization problem
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 534 - 536
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Arkowitz, M., The group of self-homotopy equivalences—A survey, Lecture Notes in Math. 1425, Springer- Verlag, 1990, 170–203.Google Scholar
2. Barcus, W. D. and Barratt, M. G., On the homotopy classification of the extensions of a fixed map, Trans. Amer. Math. Soc. 88(1958), 57–74.Google Scholar
3. Kahn, D. W., Realization problems for the group of homotopy classes of self-equivalences, Math. Ann. 220(1976), 37–46.Google Scholar
4. Maruyama, K. and Mimura, M., On the group of self-homotopy equivalences of KP2 V Sm , Mem. Fac. Sci. Kyushu Univ. Ser. A 28(1984), 65–74.Google Scholar
5. Oka, S., Finite complexes whose self-homotopy equivalences form cyclic groups, Mem. Fac. Sci. Kyushu Univ. Ser. A 34(1980), 171–181.Google Scholar
6. Toda, H., Composition method in homotopy groups of spheres, Ann. of Math. Stud. 49(1962).Google Scholar