On the Stable Hurewicz Image of Some Stunted Projective Spaces, I

Abstract

In the previous paper [3], we investigated the order of the cokernel of the stable Hurewicz homomorphism on the stunted projective space HPTM. In this paper, we consider the analogous problem for the quaternionic quasi-projective spaces. Let QP (l^n^oo) be the (4n— l)-dimensional quaternionic quasi-projective space, and QP^=QP/QP~ (2^k^ri) (denoted by Qn.n-k+1 in James [4]) be the stunted quasi-projective space. For the complex projective space CP and the quaternionic projective space HP, it is known (cf. James [5]) that QP°° is a cofiber of the projection q : CP^-^HP. Thus there is a cofiber sequence