On the 𝑝-primary obstructions to finding a cross-section

Abstract

Let q : T → B q:T \to B be a (weak) fibration, and let p p be an odd prime. In this paper, we show that the existence of a fiber-preserving map A : T → T A:T \to T having certain properties implies that the p p -primary obstructions to a cross-section of q q vanish. Assuming that q : T → B q:T \to B has a cross-section, we prove a related theorem which bears on the problem of enumerating the homotopy classes of cross-sections of q q .