Homological mirror symmetry for punctured spheres

Mohammed Abouzaid, Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov, Dmitri Orlov

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We prove that the wrapped Fukaya category of a punctured sphere S2 with an arbitrary number of points removed) is equivalent to the triangulated category of singularities of a mirror Landau-Ginzburg model, proving one side of the homological mirror symmetry conjecture in this case. By investigating fractional gradings on these categories, we conclude that cyclic covers on the symplectic side are mirror to orbifold quotients of the Landau-Ginzburg model.

Original languageEnglish (US)
Pages (from-to)1051-1083
Number of pages33
JournalJournal of the American Mathematical Society
Volume26
Issue number4
DOIs
StatePublished - 2013

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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