(n)-pairing with axes in rational homotopy

Abstract

Let $f:X\to Z$ and $g:Y\to Z$ be maps between connected pointed CW-complexes. Recall the definition of pairing with axes $f$ and $g$ due to N.Oda. In this paper, we introduce {\it (n)-pairing}, which is a generalization of {\it H(n)}-space due to Y.Félix and D.Tanré and define a family of subsets of the homotopy set of maps. We give some rational characterizations of it and illustrate some examples in Sullivan models. Also we consider about the $G(n)$-sequence of a fibration which is a generalization of $G$-sequence.