Certain generalizations of $G$-sequences and their exactness

Kee Young Lee; Moo Ha Woo; Xuezhi Zhao

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2008; 45(1): 119-131

Printed March 1, 2008

Certain generalizations of $G$-sequences and their exactness

Kee Young Lee, Moo Ha Woo, and Xuezhi Zhao

Korea University, Korea University, and Capital Normal University

Abstract

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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

MSC numbers: Primary 55Q32, 55Q52, 55P62