A GEOMETRIC CRITERION FOR GENERATING THE FUKAYA CATEGORY

被引：82

作者：

Abouzaid, Mohammld ^{[1
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2010年 / 112期

关键词：

SYMPLECTIC-GEOMETRY; COTANGENT BUNDLES;

D O I：

10.1007/s10240.010.0028.5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology Whenever the identity in symplectic cohomology lies in the Image of this map, we conclude that every Lagrangian lies in the idempotent closure of the chosen collection The main new ingredients are (1) the construction of operations on the Fukaya category controlled by discs with two outputs, and (2) the Cardy relation

引用

页码：191 / 240

页数：50

共 18 条

[1]

Abouzaid M, ARXIV10050358

[2] An open string analogue of Viterbo functoriality [J].