The Adams-Hilton model for a fibration over a sphere

Abstract

Let F→ E→ S m+1 be a fibration, where E is 1-connected and m≥2. We show how the Adams-Hilton model for the total space can be expressed succinctly in terms of the Adams-Hilton model for the induced map μ : S m xF→ F. We also explore how the Adams-Hilton model for F may be deduced from knowledge of the model for E. Lastly we examine certain iterated relative Samelson products in the mod p homotopy of F, and we extend the work of Cohen. Moore, and Neisendorfer concerning the fibers of pinch maps.