Certain generalizations of G-sequences and their exactness

Abstract

In this paper, we generalize the Gottlieb groups and the related G-sequence of those groups, and present some sufficient conditions to ensure the exactness or non-exactness of G-sequences at some terms. We also give some applications of the exactness or non-exactness of Gsequences. Especially, we show that the non-exactness of G-sequences implies the non-triviality of homotopy groups of some function spaces.