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Partially wrapped Fukaya categories of simplicial skeleta

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arxiv 1708.06038 v1 pith:37MWOV3Z submitted 2017-08-21 math.SG

Ludmil Katzarkov , Gabriel Kerr This is my paper · ORCID
classification math.SG
keywords categoriescasefukayamathbbpartiallywrappedclasscoherent
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abstract

A class of partially wrapped Fukaya categories in $T^* N$ are proven to be well defined and then studied. In the case of $N$ diffeomorphic to $\mathbb{R}^m \times \mathbb{T}^n$, it is shown that these categories provide homological mirrors to equivariant and non-equivariant categories of coherent sheaves on toric varieties. This gives a new Floer theoretic formulation of mirror symmetry in the non-complete case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Contact isotopies in the coherent-constructible correspondence

    math.AG 2025-05 accept novelty 8.0 of 10

    The nearby cycles of GKS kernels quantizing smoothed support-function Hamiltonians act on constructible sheaves by convolution with twisted polytope sheaves, matching the mirror Picard group action.

  2. Orlov and Viterbo functors in partially wrapped Fukaya categories

    math.SG 2019-08 accept novelty 8.0 of 10

    For a swappable stop the Orlov functor is spherical and its twist equals the geometric wrap-once map, while the Viterbo transfer map to a Weinstein subdomain is a homological epimorphism.

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