Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T13:54:15.391Z Has data issue: false hasContentIssue false

The group of self-homotopy equivalences of principal three sphere bundles over the seven sphere

Published online by Cambridge University Press:  24 October 2008

John W. Rutter
Affiliation:
University of Liverpool

Extract

1. The set ℰ (X) of homotopy classes of self-homotopy equivalences of a space X forms a group under composition. In this note I complete the calculation of ℰ (X) when X is a torsion free rank 2 h-space, and give ℰ (X) up to extension for the remaining principal S3 bundles over S7.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)James, I. M.On sphere bundles over spheres. Comment. Math. Helv. 35 (1961), 126135.CrossRefGoogle Scholar
(2)Hilton, P. J. and Roitberg, J.On principal S 3-bundles over spheres. Ann. of Math. 90 (1969), 91107.CrossRefGoogle Scholar
(3)Oka, S., Sawashita, M. and Sugawara, M.On the group of self equivalences of a mapping cone. Hiroshima Math. J. 4 (1974), 928.CrossRefGoogle Scholar
(4)Rutter, J. W.Groups of self homotopy equivalences of induced spaces. Comment. Math. Helv. 45 (1970), 236–55.CrossRefGoogle Scholar
(5)Sawashita, N.On the group of self-equivalences of the product of spheres. Hiroshima Math. J. 5 (1975), 6986.CrossRefGoogle Scholar
(6)Toda, H. Composition methods in homotopy groups of spheres. Ann. of Math. Studies 49 (1962) (Princeton).Google Scholar
(7)Zabrodsky, A.The classification of simply connected H-spaces with three cells: I. Math. Scand. 30 (1972), 193210.CrossRefGoogle Scholar