Certain generalizations of $G$-sequences and their exactness
Bull. Korean Math. Soc. 2008 Vol. 45, No. 1, 119-131 Printed March 1, 2008
Kee Young Lee, Moo Ha Woo, and Xuezhi Zhao Korea University, Korea University, and Capital Normal University
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 $G$-sequences. Especially, we show that the non-exactness of $G$-sequences implies the non-triviality of homotopy groups of some function spaces.
Keywords : Gottlieb group, $G$-sequence, homotopy group