2016/04/30 by Zachary Sylvan · 45 citations
Mathematics · #Algebraic structures and combinatorial models #Boundary (topology) #Class (philosophy) #Disjoint sets #Domain (mathematical analysis) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic geometry #math.SG
paper · pdf · doi:10.1112/topo.12088
published in Journal of Topology 12(2), 372-441 (Wiley) · v3: version accepted by the Journal of Topology. Some of the more routine proofs have been omitted
openalex created_date 2016/06/24 · openalex publication_date 2019/01/30 · arxiv created 2019/02/01 · arxiv updated 2019/02/06 · openalex updated_date 2026/08/06
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.