Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1997; 34(3): 653-659

Printed September 1, 1997

Copyright © The Korean Mathematical Society.

An extension of Gottlieb groups

Kee Young Lee and Moo Ha Woo

Taejon National University of Technology and Korea University

Abstract

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.

Keywords: evaluation groups, evaluation group of a map

MSC numbers: 55P45

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