Projective Homotopy Classes of Stiefel Manifolds

Abstract

Given a homotopy class [f] in π n (X), we say that [f] is projective if and only if there is a homotopy commutative factorization where v is the standard double covering. We then denote by the subset of projective homotopy classes in π n (X). The notion of projective homotopy classes was studied in the author's thesis [ 5 ], and the projective homotopy classes for spheres in the stable range, up through the 3-stem were calculated in [ 6 ].