Consequences of the kahn–priddy theorem in homotopy and geometry

Abstract

Much recent attention has been given to geometric representation of elements of the stable homotopy groups of spheres, π* s A particular example concerns non-singular bilinear maps ℝ m +1 × ℝ n +1 → ℝ m+n +1− p ; on restriction and normalisation these become biskew maps S m × S n ℝ S m+n-p ;. Now the Hopf construction ℋ applied to any map f: S m × S n → S m+n-p yields