Homological mirror symmetry for punctured spheres

By M. Abouzaid, D. Auroux, Alexander I. Efimov, L. Katzarkov, Dmitri Orlov. 2011

91 citations recorded by the source corpus.

We prove that the wrapped Fukaya category of a punctured sphere (S 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9e302a0f2e1e29bac813f826f1928be524c0b5d6

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A Beginner’s Introduction to Fukaya Categories (2013, unknown): “ computed in order to fully determine the A∞-structure up to homotopy. Symplectic manifolds whose Fukaya categories have been determined in this manner include (but are not limited to) pairs of pants [9], genus 2 curves [44], and Calabi-Yau hypersurfaces in projective space [46]. 4.5. An application”
The monotone wrapped Fukaya category and the open-closed string map (2012, methodology): “The wrapped Fukaya category W(E) of a non-compact convex symplectic manifold E, introduced in [23, 8] in the exact setup, is of increasing importance both in symplectic topology (topology of Stein manifolds [29], the nearby Lagrangian conjecture [5]) and in Homological Mirror Symmetry [6, 44].”
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, background): “These results provide a geometric foundation for mirror constructions that have appeared in the recent literature [11, 28, 27, 40, 42, 1, 20].”