Work

Triangulation, Persistence, and Fukaya Categories

Year: 2026

Type: book

Abstract: This memoir introduces a new algebraic notion: that of a triangulated persistence category (TPC), which refines the notion of a triangulated category in the same sense that a persistence module refines that of a vector space.The spaces of morphisms of such a TPC are persistence modules, and the 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 we apply this 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.

Source: Memoirs of the European Mathematical Society

DOI: 10.4171/mems/28

Authors: Paul Biran, Octav Cornea, Jun Zhang

Institutions: ETH Zurich, Université de Montréal, University of Science and Technology of China

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Centre de Recherches Mathématiques, National Natural Science Foundation of China, University of Science and Technology of China, Natural Sciences and Engineering Research Council of Canada

Awards: G1945911282, G3114601955