GENERALIZED GOTTLIEB SUBGROUPS AND SERRE FIBRATIONS

Title & Authors
GENERALIZED GOTTLIEB SUBGROUPS AND SERRE FIBRATIONS
Kim, Jae-Ryong;

Abstract
Let $\small{{\pi}:E{\rightarrow}B}$ be a Serre fibration with fibre F. We prove that if the inclusion map $\small{i:F{\rightarrow}E}$ has a left homotopy inverse r and $\small{{\pi}:E{\rightarrow}B}$ admits a cross section $\small{{\rho}:B{\rightarrow}E}$, then $\small{G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)}$. This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in [8]. Using this result, we will prove that $\small{{\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)}$ for the function space $\small{X^A}$ from a space A to a weak $\small{H_*}$-space X where the evaluation map $\small{{\omega}:X^A{\rightarrow}X}$ is regarded as a fibration.
Keywords
generalized Gottlieb subgroups;Serre fibrations;G-sequence;
Language
English
Cited by
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