2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229809Adapting a construction of D Salamon involving the U(1) vortex equations, we explore the properties of a Floer theory for 3-manifolds that fiber over S^1 which exhibits several parallels with monopole Floer homology, and in all likelihood coincides with it. The theory fits into a restricted analogue of a TQFT in which the cobordisms are required to be equipped with Lefschetz fibrations, and has connections to the dynamics of surface symplectomorphisms.This is the version published by Algebraic & Geometric Topology on 21 October 2006Symplectic GeometryGeometric Topology57R57, 53D40, 57R56text