Given a ribbon graph Γ with some extra structure, we define, using constructible sheaves, a dg category CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by Γ. When Γ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from Γ a one-dimensional algebraic stack XΓ with toric components. We prove that our model is equivalent to Perf(XΓ), the dg category of perfect complexes on XΓ.
CITATION STYLE
Sibilla, N., Treumann, D., & Zaslow, E. (2014). Ribbon graphs and mirror symmetry. Selecta Mathematica, New Series, 20(4), 979–1002. https://doi.org/10.1007/s00029-014-0149-7
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