Let @math be a Laurent polynomial in @math variables, and let @math be a generic smooth fiber of @math . In RSTZ Ruddat-Sibilla-Treumann-Zaslow give a combinatorial recipe for a skeleton for @math . In this paper, we show that for a suitable exact symplectic structure on @math , the RSTZ-skeleton can be realized as the Liouville Lagrangian skeleton.
@cite_5: Inspired by the geometry of wrapped Fukaya categories, we introduce the notion of wrapped microlocal sheaves. We show that traditional microlocal sheaves are equivalent to functionals on wrapped microlocal sheaves, in analogy with the expected relation of infinitesimal to wrapped Fukaya categories. As an application, we calculate wrapped microlocal sheaves on higher-dimensional pairs of pants, confirming expectations from mirror symmetry.
@cite_14: We prove a homological mirror symmetry equivalence between an @math -brane category for the pair of pants, computed as a wrapped microlocal sheaf category, and a @math -brane category for a mirror LG model, understood as a category of matrix factorizations. The equivalence improves upon prior results in two ways: it intertwines evident affine Weyl group symmetries on both sides, and it exhibits the relation of wrapped microlocal sheaves along different types of Lagrangian skeleta for the same hypersurface. The equivalence proceeds through the construction of a combinatorial realization of the @math -model via arboreal singularities. The constructions here represent the start of a program to generalize to higher dimensions many of the structures which have appeared in topological approaches to Fukaya categories of surfaces.
@cite_6: 
The skeleton for @math dimensional pair-of-pants @math has been studied by Nadler @cite_5 , where a higher dimensional analog of Figure is constructued. A @math -symmetric skeleton for @math is constructed by Gammage-Nadler @cite_14 , where @math is the symmetric group. With the technique of tropical phase variety of Kerr-Zharkov @cite_6 , we hope to find other Lagrangian skeleta @math for @math , where @math indicating the number of dominant terms in the defining equation of @math .