Homological mirror symmetry for punctured spheres

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

Research output: Contribution to journalArticle

22 Citations (Scopus)

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

Fingerprint

Mirror Symmetry
Ginzburg-Landau Model
Mirror
Mirrors
Triangulated Category
Grading
Orbifold
Quotient
Fractional
Cover
Singularity
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Homological mirror symmetry for punctured spheres. / Abouzaid, Mohammed; Auroux, Denis; Efimov, Alexander I.; Katzarkov, Ludmil; Orlov, Dmitri.

In: Journal of the American Mathematical Society, Vol. 26, No. 4, 2013, p. 1051-1083.

Research output: Contribution to journalArticle

Abouzaid, Mohammed ; Auroux, Denis ; Efimov, Alexander I. ; Katzarkov, Ludmil ; Orlov, Dmitri. / Homological mirror symmetry for punctured spheres. In: Journal of the American Mathematical Society. 2013 ; Vol. 26, No. 4. pp. 1051-1083.
@article{c96fa4302ed54da29b0a5f1ac222632f,
title = "Homological mirror symmetry for punctured spheres",
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.",
author = "Mohammed Abouzaid and Denis Auroux and Efimov, {Alexander I.} and Ludmil Katzarkov and Dmitri Orlov",
year = "2013",
doi = "10.1090/S0894-0347-2013-00770-5",
language = "English (US)",
volume = "26",
pages = "1051--1083",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "4",

}

TY - JOUR

T1 - Homological mirror symmetry for punctured spheres

AU - Abouzaid, Mohammed

AU - Auroux, Denis

AU - Efimov, Alexander I.

AU - Katzarkov, Ludmil

AU - Orlov, Dmitri

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84880368665&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880368665&partnerID=8YFLogxK

U2 - 10.1090/S0894-0347-2013-00770-5

DO - 10.1090/S0894-0347-2013-00770-5

M3 - Article

VL - 26

SP - 1051

EP - 1083

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

SN - 0894-0347

IS - 4

ER -