Ribbon graphs and mirror symmetry

Nicolò Sibilla*, David Treumann, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)979-1002
Number of pages24
JournalSelecta Mathematica, New Series
Volume20
Issue number4
DOIs
StatePublished - Jan 1 2014

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Keywords

  • Constructible sheaves
  • Homological mirror symmetry
  • Ribbon graphs

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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