On partially wrapped Fukaya categories

By Zachary Sylvan. Journal of Topology, 2016

100 citations recorded by the source corpus.

We define a new class of symplectic objects called ‘stops’, which, roughly speaking, are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a compatible open book. To a Liouville domain with a collection of disjoint stops, we assign an A∞ ‐category called its partially wrapped Fukaya category. An exact Landau–Ginzburg model gives rise to a stop, and the corresponding partially wrapped Fukaya category is meant to agree with the Fukaya category one is supposed to assign to the Landau–Ginzburg model. As evidence, we prove a formula that relates these partially wrapped Fukaya categories to the wrapped Fukaya category of the underlying Liouville domain. This operation is mirror to removing a divisor.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c23a3141913f1ab2c4af979da84a50b85f103590

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Citations in the corpus

Sectorial descent for wrapped Fukaya categories (2018, methodology): “This statement builds on two prior results: Abouzaid–Seidel [5] proved that for Lefschetz fibrations, the wrapped Fukaya category of the total space is a localization of the Fukaya–Seidel category, and Sylvan [42] showed (under certain hypotheses) that the partially wrapped Fukaya category of a Liou”
Microlocal Morse theory of wrapped Fukaya categories (2018, background): “This category is defined and studied in [7, 52, 19, 20], and one has particularly good control over it when X is Weinstein and Λ is a (possibly singular) isotropic.”
Auslander orders over nodal stacky curves and partially wrapped Fukaya categories (2017, background): “t identiﬁes the following triangulated categories, all deﬁned over Z: F(Td) ≃Perf(Cd) (0.1) W(Td) ≃Db(CohCd). (0.2) In recent years, a theory of partially wrapped Fukaya categories was developed ([2],[24], [10], [8]). This depends onanextrachoice ofaLegendrian submanifoldΛattheboundaryof X. In the c”
Geometric generation of the wrapped Fukaya category of Weinstein manifolds and sectors (2017, result): “aid and P. Seidel [4]. The deﬁnition of the wrapped Fukaya category was further extended to the relative case by Z. Sylvan, who introduced the notions of stop and partially wrapped Fukaya category in [38], and by S. Ganatra, J. Pardon and V. Shende, who later introduced the similar notion of Liouvil”