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WE say that a self-map / : HP"-* HP" of infinite quaternionic projective space has degree k, deg (f) = k, if the induced map of QMP°° =* S is of degree k in the usual sense. It is well known that deg (/) is zero or an odd square integer [6]. The self-maps of HP°° = BS which are induced from Lie groups endomorphisms of S are easily seen to be of degree zero or one. Using localization techniques and methods from 6tale homotopy theory, D. Sullivan was able to construct self-maps of HP" of any given odd square degree [14]. To complete the picture, we present a proof of the following theorem.

THE HOMOTOPY CLASSIFICATION OF SELF-MAPS OF INFINITE QUATERNIONIC PROJECTIVE SPACE