The evaluation map and EHP sequences

Abstract

Let L(B, X) be the space of maps from B (the reduced suspension of B) to X with the compact-open topology, let S\ B-> X and L(B, X; /) the path component of L(B, X) containing /. For nice spaces the evaluation map : L(B, X,s)->X defined by (f) = /(*) is a fibration and gives rise to a long exact sequence in homotopy. The purpose of this paper is to show that the boundary map in that long exact sequence can be given by a generalized Whitehead product and that the sequence generalizes the EHP sequence of G. W. Whitehead.