The rigidity problem for stable spaces

Kahn, Donald W.

doi:10.1090/S0002-9939-1979-0529230-4

The rigidity problem for stable spaces
HTML articles powered by AMS MathViewer

by Donald W. Kahn

Proc. Amer. Math. Soc. 75 (1979), 139-144

DOI: https://doi.org/10.1090/S0002-9939-1979-0529230-4

PDF | Request permission

Abstract:

This note treats the problem of when the group of homotopy self-equivalences of a space is trivial. For stable spaces, with finitely many nonvanishing homotopy groups, we give a complete solution in an inductive sense. One of the consequences of this result is that for any stable space, with precisely two nonvanishing homotopy groups, the group of self-equivalences is nontrivial.

References

P. J. Hilton, An introduction to homotopy theory, Cambridge Tracts in Mathematics and Mathematical Physics, No. 43, Cambridge, at the University Press, 1953. MR 0056289
Donald W. Kahn, Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432–450. MR 150777, DOI 10.1090/S0002-9947-1963-0150777-X
Donald W. Kahn, The group of homotopy equivalences, Math. Z. 84 (1964), 1–8. MR 170344, DOI 10.1007/BF01112204
Donald W. Kahn, The group of stable self-equivalences, Topology 11 (1972), 133–140. MR 286103, DOI 10.1016/0040-9383(72)90027-4
Donald W. Kahn, Realization problems for the group of homotopy classes of self-equivalences, Math. Ann. 220 (1976), no. 1, 37–46. MR 402730, DOI 10.1007/BF01354527
Jean-Pierre Serre, Cohomologie modulo $2$ des complexes d’Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198–232 (French). MR 60234, DOI 10.1007/BF02564562
Dennis Sullivan, Infinitesimal computations in topology, Inst. Hautes Études Sci. Publ. Math. 47 (1977), 269–331 (1978). MR 646078
Clarence W. Wilkerson, Applications of minimal simplicial groups, Topology 15 (1976), no. 2, 111–130. MR 402737, DOI 10.1016/0040-9383(76)90001-X