Year: 2009
Type: article
Abstract: Let ${\pi}:E{\rightarrow}B$ be a Serre fibration with fibre F. We prove that if the inclusion map $i:F{\rightarrow}E$ has a left homotopy inverse r and ${\pi}:E{\rightarrow}B$ admits a cross section ${\rho}:B{\rightarrow}E$ , then $G_n(E,F){\cong}{\pi}_n(B){\oplus}G_n(F)$ . 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 ${\pi}_n(X^A){\cong}{\pi}_n(X){\oplus}G_n(F)$ for the function space $X^A$ from a space A to a weak $H_*$ -space X where the evaluation map ${\omega}:X^A{\rightarrow}X$ is regarded as a fibration.
Author: Jae-Ryong Kim
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2088629976