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This article is cited in 29 scientific papers (total in 29 papers)
Homological mirror symmetry for punctured spheres
M. Abouzaida, D. Aurouxb, A. I. Efimovc, L. Katzarkovde, D. Orlovc a Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
b Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
c Algebraic Geometry Section, Steklov Mathematical Institute, Russian Academy of Sciences, 8 Gubkin Street, Moscow 119991, Russia
d Department of Mathematics, Universität Wien, Garnisongasse 3, Vienna A-1090, Austria
e University of Miami, P.O. Box 249085, Coral Gables, Florida 33124-4250
Abstract:
We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2}$ 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.
Received: 22.03.2011 Revised: 02.03.2013
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