Lagrangian shadows and triangulated categories
By: Paul Biran, Octav Cornea, Egor Shelukhin
Contributors: Cornea, O. (Octavian), 1966- author; Shelukhin, Egor, author; Société mathématique de France
Series: Astérisque -- numéro 426; Astérisque -- 426.
Publisher: Société Mathématique de France
Published: 2021
Place of publication: Paris, France
Language: eng
Number of pages: 128
ISBN-13: 9782856299401
Copyright date: 2021
Subjects: Lagrange spectrum; Triangulated categories
Description: We introduce new metrics on spaces of Lagrangian submanifolds, not necessarily in a fixed Hamiltonian isotopy class. Our metrics arise from measurements involving Lagrangian cobordisms. We also show that splitting Lagrangians through cobordism has an energy cost and, from this cost being smaller than certain explicit bounds, we deduce some forms of rigidity of Lagrangian intersections. We also fit these constructions in the more general algebraic setting of triangulated categories, independent of Lagrangian cobordism. As a main technical tool, we develop aspects of the theory of (weakly) filtered A∞-categories.
Notes: Includes bibliographical references (pages [125]-128).

Text in English, with abstracts in English and French.