Bulk Deformations of Open Topological String Theory

We present a general method to construct bulk-deformed open topological string theories from Landau-Ginzburg models. To this end we obtain a weak version of deformation quantisation, and we show how this together with the technique of homological perturbation allows to explicitly compute all bulk-deformed open topological string amplitudes at tree-level before tadpole-cancellation. Our approach is based on a coherent treatment of the problem in terms of the fundamental A (a)- and L (a)-structures involved.