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 its
wrapped Fukaya category in a suitable model by reconstructing it from those of various pairs
of pants. The pieces are glued together in the sense that the restrictions of the wrapped
Floer 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 singularities
of the mirror Landau-Ginzburg model can also be constructed in the same way from local
ane pieces that are mirrors of the pairs of pants.