Resumen de Ribbon graphs and mirror symmetry

Nicolò Sibilla, David Treumann, Eric Zaslow

• Given a ribbon graph ΓΓ with some extra structure, we define, using constructible sheaves, a dg category CPM(Γ)CPM(Γ) meant to model the Fukaya category of a Riemann surface in the cell of Teichmüller space described by Γ.Γ. When ΓΓ is appropriately decorated and admits a combinatorial “torus fibration with section,” we construct from ΓΓ a one-dimensional algebraic stack X˜ΓX~Γ with toric components. We prove that our model is equivalent to Perf(X˜Γ)Perf(X~Γ) , the dg category of perfect complexes on X˜ΓX~Γ .