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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Mirror symmetry for honeycombs


Authors: Benjamin Gammage and David Nadler
Journal: Trans. Amer. Math. Soc. 373 (2020), 71-107
MSC (2010): Primary 14J33, 53D37
DOI: https://doi.org/10.1090/tran/7909
Published electronically: September 10, 2019
MathSciNet review: 4042869
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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.


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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
Email: nadler@math.berkeley.edu

DOI: https://doi.org/10.1090/tran/7909
Keywords: Mirror symmetry, microlocal sheaves
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.
Article copyright: © Copyright 2019 American Mathematical Society