2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220778Given a closed 3--manifold $Y$, we show that the Heegaard Floer homology determines whether $Y$ fibres over the circle with a fibre of negative Euler characteristic. This is an analogue of an earlier result about knots proved by Ghiggini and the author.Version 3: 16 pages, 1 figure. This version incorporates the corrigendum to a previous paper. To appear in American Journal of Mathematics. Version 2: Corrects some mistakes in Version 1. The last section of Version 1 is replaced using a quite different and much simpler method. Exposition improved according to the referee's suggestionsGeometric Topology57R58, 57M27, 57R30text