THE FIRST NON-VANISHING GROUP OF AN (n + 1)-AD

Abstract

This chapter presents the definition of the generalized Whitehead products in an (n+1)-ad and discusses the first non-vanishing homotopy group of a complete CW-(n–1)-ad in terms of these products. This expression involves n-fold products. Thus, the first non-vanishing group of a tetrad is described by means of triple products, of a 5-ad by quadruple products and so on. The chapter discusses the conditions under which the product homomorphism θ: πm(A, C) ⊗ πq–m+1 (B, C) → πq(X,A, B) for a triad is an isomorphism onto, or merely onto, when q takes on a range of values beyond the first for which πq(X, A, B) ≠ 0.