On classifying Hurewicz fibrations and fibre bundles over polyhedron bases

Mathematics – Algebraic Topology

Scientific paper

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17 pages, 2 figures

Scientific paper

Let $f:E\longrightarrow O$ 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.

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