2011/03/12 by Nicolò Sibilla, Nicoló Sibilla, Sibilla, Nicoló +4 · 5 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG) #math.AG #math.AT #math.SG
paper · pdf · doi:10.48550/arxiv.1103.2462
28 pages
arxiv created 2011/03/12 · openalex publication_date 2011/03/12 · arxiv updated 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \widetildeXΓ with toric components. We prove that our model is equivalent to Perf(\widetildeXΓ), the dg category of perfect complexes on \widetildeXΓ.