The Weinstein skeleton conjecture for toric hypersurface mirrors

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Suppose △\triangle is vertex-simplicial and △∨\triangle^\vee is facet-simplicial. Let Z∞∨Z^\vee_\infty be the large volume limit and let Λ∞\Lambda^\infty be the associated Legendrian boundary. Toric hypersurface skeleton conjecture. There is a Weinstein structure on Z∞∨Z^\vee_\infty whose Lagrangian skeleton is homeomorphic to Λ∞\Lambda^\infty. The sheaf of Fukaya categories on this skeleton is equivalent to the Kashiwara–Schapira sheaf on Λ∞\Lambda^\infty. This conjecture identifies the proposed Legendrian skeleton with a Weinstein skeleton and predicts compatibility of their categorical sheaves; the supplied source gives no evidence of resolution.

References

Primary source

David Treumann and Eric Zaslow, “Polytopes and Skeleta”, arXiv:1109.4430 (2011).

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