Work

Homological mirror symmetry for punctured spheres

Year: 2011

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1103.4322

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

Institutions: Columbia University, University of California, Berkeley, Russian Academy of Sciences, Steklov Mathematical Institute, University of Vienna, University of Miami

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2949731985

Cites: 35

Cited by: 5

Related to: 20