Ribbon graphs and mirror symmetry

Nicolò Sibilla*, David Treumann, Eric Zaslow

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Citations (Scopus)

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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Mirror Symmetry
ribbons
mirrors
symmetry
Graph in graph theory
Algebraic Stacks
Constructible
Fibration
Sheaves
Riemann Surface
Torus
Cell
cells
Model

Keywords

  • Constructible sheaves
  • Homological mirror symmetry
  • Ribbon graphs

ASJC Scopus subject areas

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

Cite this

Sibilla, Nicolò ; Treumann, David ; Zaslow, Eric. / Ribbon graphs and mirror symmetry. In: Selecta Mathematica, New Series. 2014 ; Vol. 20, No. 4. pp. 979-1002.
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Ribbon graphs and mirror symmetry. / Sibilla, Nicolò; Treumann, David; Zaslow, Eric.

In: Selecta Mathematica, New Series, Vol. 20, No. 4, 01.01.2014, p. 979-1002.

Research output: Contribution to journalArticle

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