AN EXTENSION OF GOTTLIEB GROUPS

AN EXTENSION OF GOTTLIEB GROUPS

In this paper, we extend the Gottlieb groups of a space to the Gottlieb groups of a map and show some properties of those groups. Especially, We show the 2nd Gottlieb group of a map is contained in the center of the homotopy group of the map and show $G_n(F) = \pi_n(f)$ for an H-map f between H-spaces. We also show the Gottlieb subgroups $G_n(A), G_n(X) and G_n(f)$ make a sequence if the map $f : A \to X$ has a right homotopy inverse.

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