A Lagrangian Pictionary

Abstract

The purpose of this paper is to describe a dictionary geometry <--> algebra in Lagrangian topology. As a by-product we obtain a tautological (in a sense explained in the body of the paper) proof of a folklore conjecture (sometimes attributed to Kontsevich) claiming that the objects and structure of the derived Fukaya category can be represented through immersed Lagrangians. Our construction is based on certain Lagrangian cobordism categories endowed with a structure called "surgery models".

arXiv comment53 figures

References in corpus (10)

• Compactness results in Symplectic Field Theory
• A stable infinity-category of Lagrangian cobordisms
• Floer homology of Lagrangians in clean intersection
• Sheaf Quantization of Lagrangians and Floer cohomology
• Categorification of Seidel's representation
• Invariants of Lagrangian cobordisms via spectral numbers
• Structure of $J$-holomorphic disks with immersed Lagrangian boundary conditions
• Lagrangian cobordism groups of higher genus surfaces
• Fukaya categories of Lagrangian cobordisms and duality
• A distance expanding flow on exact Lagrangian cobordism classes