On the stable homotopy of quaternionic and complex projective spaces.

Abstract

Let the image in H 4 k ( QP ∞ : Z ) = Z {H_{4k}}({\operatorname {QP} ^\infty }:Z) = Z of stable homotopy under the Hurewicz homomorphism be h ( k ) ⋅ Z h(k) \cdot Z . Using the Adams spectral sequence for the 2 2 -primary stable homotopy of quaternionic and complex projective spaces it is shown that h ( k ) h(k) is ( 2 k ) ! (2k)! if k k is even and is ( 2 k ) ! / 2 (2k)!/2 if k k is odd.