Lagrangian Cobordism and Fukaya Categories
Symplectic Geometry
2018-08-28 v3 Geometric Topology
Abstract
Given a symplectic manifold M, we consider a category with objects finite ordered families of Lagrangian submanifolds of M (subject to certain additional constraints) and with morphisms Lagrangian cobordisms relating them. We construct a functor that maps this category to a variant of the derived Fukaya category of M in a way that takes into account the triangulated structure of the latter.
Keywords
Cite
@article{arxiv.1304.6032,
title = {Lagrangian Cobordism and Fukaya Categories},
author = {Paul Biran and Octav Cornea},
journal= {arXiv preprint arXiv:1304.6032},
year = {2018}
}
Comments
103 pages; subsection 4.3.2 (which was introduced in version 2) is revised with more details and corrected versions of the technical Lemma 4.3.3 and Corollary 4.3.4; statements and formulas unchanged in the rest of the paper (see Remark 4.3.5 for details)