Triangulation, Persistence, and Fukaya Categories

von Paul Biran, Octav Cornea, Jun Zhang

Hardcover

Kurzbeschreibung des Verlags

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.

• Reihe: Memoirs of the European Mathematical Society
• Themen: Mathematik und Naturwissenschaften Mathematik Geometrie Differentielle und Riemannsche Geometrie
• ISBN: 9783985471072
• Sprache: Englisch
• Erscheinungsdatum: 01.06.2026
• Größe: 24 x 17 cm
• Verlag: EMS Press