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arXiv · 2304.01785

Triangulation, Persistence, and Fukaya categories

Paul Biran·Octav Cornea·Jun Zhang
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Abstract

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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Paul Biran, Octav Cornea, Jun Zhang. 2023-04-04. Triangulation, Persistence, and Fukaya categories. https://arxiv.org/abs/2304.01785

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