Ganea fibrations
The authors define and study a general family of fibrations called \(n\text{-LS}\) fibrations. Denote by \(p_n:G_n(X)\to X\) the classical Ganea fibration associated to a space \(X\). Then a fibration \(Q:E\to X\) is called \(n\text{-LS}\) if there are morphisms \(s:G_n(X)\to E\) and \(t:E\to G_n(X)\) such that \(qs=p_n\) and \(p_nt=q\). A space \(X\) has Lyusternik-Shnirel'man category \(\leq n\) if and only if some \(n\text{-LS}\) fibration with base \(X\) has a section. The text contains constructions of generic family of \(n\text{-LS}\) fibrations, and the authors recover in this way the characterization of LS category in rational homotopy given by Felix-Halperin and Lemaire.
scientific article; zbMATH DE number 1266861