Mirror symmetry for honeycombs
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- by Benjamin Gammage and David Nadler PDF
- Trans. Amer. Math. Soc. 373 (2020), 71-107 Request permission
Abstract:
We prove a homological mirror symmetry equivalence between the $A$-brane category of the pair of pants, computed as a wrapped microlocal sheaf category, and the $B$-brane category of its 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 $A$-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.References
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Additional Information
- Benjamin Gammage
- Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
- Address at time of publication: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
- Email: bgammage@math.berkeley.edu
- David Nadler
- Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720-3840
- MR Author ID: 620327
- Email: nadler@math.berkeley.edu
- Received by editor(s): December 7, 2018
- Received by editor(s) in revised form: April 12, 2019
- Published electronically: September 10, 2019
- Additional Notes: The first author is grateful to the NSF for the support of a Graduate Research Fellowship.
The second author is grateful for the support of grant DMS-1502178. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 71-107
- MSC (2010): Primary 14J33, 53D37
- DOI: https://doi.org/10.1090/tran/7909
- MathSciNet review: 4042869