We consider the Fukaya-Floer $A_\infty$-structures arising from a basis of thimbles in a Lefschetz fibration. Particular attention is paid to the relation between these structures in the total space of the fibration, and their counterparts in the fibre.
"Fukaya $A_\infty$-structures associated to Lefschetz fibrations. I." J. Symplectic Geom. 10 (3) 325 - 388, September 2012.