Rational higher order Whitehead products of mapping spaces and defining systems

Abstract

This paper gives an algebraic description of rational higher order Whitehead products in mapping spaces. Given a Sullivan representative of the base map, we introduce defining systems in the corresponding derivation complex. The main result shows that, under the standard identification between rational homotopy groups of mapping spaces and the cohomology of the derivation complex, rational higher order Whitehead products are given exactly by the cohomology classes represented by the associated derivation brackets. The examples show how choices of defining systems produce non-trivial elements and indeterminacy.