The rigidity problem for stable spaces

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.