TY  - BOOK
AU  - Biran,Paul
AU  - Cornea,Octav
AU  - Shelukhin,Egor
TI  - Lagrangian shadows and triangulated categories
T2  - Asterisque
SN  - 9782856299401
U1  - 514.72 23
PY  - 2021///
CY  - Paris: 
PB  - Societe Mathematique de France
KW  - Lagrange Spectrum
KW  - Lagrange
KW  - Triangulated Categories
KW  - Lagrangian Cobordism
N1  - Includes bibliographical references
N2  - Under certain assumptions (such as weak exacteness or monotonicity) we show that splitting Lagrangians through cobordism has an energy cost and, from this cost being smaller than certain explicit bounds, we deduce some strong forms of rigidity of Lagrangian intersections. As a consequence, we construct some new pseudo-metrics and metrics on certain classes of Lagrangian submanifolds. We also fit these constructions in a more general setting, independent of Lagrangian cobordism. As a main technical tool, we develop aspects of the theory of (weakly) filtered A-infinity categories
ER  -