On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Abstract

Let $f:E⟶O$ be a Hurewicz fibration with a fiber space $F_{r_o}$ and a lifting function $L_f$. The \emph{$Lf-$function} ${\Theta }_{L_f}$ of $f$ is defined by the restriction map of $L_f$ on the space $\Omega (O,r_o)\times F_{r_o}\times \{1\}$. The purpose of this paper is to give some results which show the role of $Lf-$functions in finding a fiber homotopically equivalent relation between two fibrations, over a common polyhedron base. Furthermore we will prove the equivalently between our results and Dold's theorem in fiber bundles, over a common suspension base of polyhedron spaces.

17 pages, 2 figures

References in corpus (1)

• An index theorem for Wiener--Hopf operators