2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63332We use slicing by nongeneric pencils of hypersurfaces and prove a new theorem of Lefschetz type for singular non compact spaces, at the homotopy level. As applications, we derive results on the topology of the fibres of polynomial functions or the topology of complements of hypersurfaces in $\mathbb C^n$.to appear in Internat. J. MathAlgebraic GeometryComplex Variables32S50, 14F35, 14F45text