  Adapting 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.
