Higher order Whitehead products and Postnikov systems
Gerald J. Porter · Illinois Journal of Mathematics · 1967
In an arcwise connected CW-complex, higher order Whitehead products are determined, as areall homotopy operations, by the Postnikov invariants of the space.This fact has been used implicitly in [3] to prove that certain products are non-zero.In this note we calculate this relationship explicitly.This is done by relating Whitehead products and classical obstruction theory.Let P(C) denote n-dimensional complex projective space.As an application we show that if e (P(C) is a generator, then the set of (n H-1 order White- head products [...., e] equals (n-F 1)! , where is a generator of ,+ (P(C) ).The author would like to thank M. Arkowitz for raising the question about P(C) which led to this note.Let T denote the subset of the cartesian product, X : S , consisting of those points with at least one coordinate at a base point.We assume through- out that n > 1, all i, and } 2. Choose a generator H( X S; Z), where, N n.Given a map g" T