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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.

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