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Triangulation, Persistence, and Fukaya categories

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arxiv 2304.01785 v2 pith:F3EYAPH7 submitted 2023-04-04 math.SG math.AT

Paul Biran , Octav Cornea , Jun Zhang This is my paper · ORCID
classification math.SGmath.AT
keywords categorypersistencefukayanotionrefinementspacespacestriangulated
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This paper introduces a new algebraic notion - triangulated persistence category (TPC) - that refines that of triangulated category in the same sense that a persistence module is a refinement of the notion of a vector space. The spaces of morphisms of such a TPC are persistence modules and this category is endowed with a class of weighted distinguished triangles. Under favourable conditions we show that the derived Fukaya category admits a TPC refinement and this is applied to deduce a global rigidity result for spaces of compact, exact Lagrangians in certain Liouville manifolds: we construct a metric on this space with intrinsic symplectic properties.

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  1. Density of fibers for the filtered Fukaya category of $T^*N$

    math.SG 2026-02 conditional novelty 7.0 of 10

    Iterated cones of cotangent fibers are dense in the filtered Fukaya category with respect to the interleaving distance, with a dim N + 1-cone improvement.

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