Homological mirror symmetry for open Riemann surfaces from pair-of-pants decompositions

Given a punctured Riemann surface with a pair-of-pants decomposition, we compute itswrapped Fukaya category in a suitable model by reconstructing it from those of various pairsof pants. The pieces are glued together in the sense that the restrictions of the wrappedFloer complexes from two adjacent pairs of pants to their adjoining cylindrical piece agree.The A infinity-structures are given by those in the pairs of pants. The category of singularitiesof the mirror Landau-Ginzburg model can also be constructed in the same way from localane pieces that are mirrors of the pairs of pants