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

Abstract

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 3 is of degree k in the usual sense. It is well known that deg (/) is zero or an odd square integer The self-maps of HP = BS 3 which are induced from Lie groups endomorphisms of S 3 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.