Generalized Gottlieb subgroups and Serre fibrations
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Let π : E → B be a Serre fibration with fibre F. We prove that if the inclusion map i: F→E has a left homotopy inverse r and π : E → B admits a cross section ρ : B →E then Gn(E,F) π_n(B) G_n(F). This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in cite{LW 1}. Using this result, we will prove that π_n(X^A) pi_n(X) G_n(F) for the function space X^A from a space A to a weak H-space X where the evaluation map ω :X^A→ X is regarded as a fibration.
Abstract
Let π : E → B be a Serre fibration with fibre F. We prove that if the inclusion map i: F→E has a left homotopy inverse r and π : E → B admits a cross section ρ : B →E then Gn(E,F) π_n(B) G_n(F). This is a generalization of the case of trivial fibration which has been proved by Lee and Woo in cite{LW 1}. Using this result, we will prove that π_n(X^A) pi_n(X) G_n(F) for the function space X^A from a space A to a weak H-space X where the evaluation map ω :X^A→ X is regarded as a fibration.
참고문헌 (13)
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