## Geometry & Topology

### Holomorphic Lagrangian branes correspond to perverse sheaves

Xin Jin

#### Abstract

Let $X$ be a compact complex manifold, $Dcb(X)$ be the bounded derived category of constructible sheaves on $X$, and $Fuk(T∗X)$ be the Fukaya category of $T∗X$. A Lagrangian brane in $Fuk(T∗X)$ is holomorphic if the underlying Lagrangian submanifold is complex analytic in $T∗Xℂ$, the holomorphic cotangent bundle of $X$. We prove that under the quasiequivalence between $Dcb(X)$ and $DFuk(T∗X)$ established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.

#### Article information

Source
Geom. Topol., Volume 19, Number 3 (2015), 1685-1735.

Dates
Revised: 18 July 2014
Accepted: 16 August 2014
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510858773

Digital Object Identifier
doi:10.2140/gt.2015.19.1685

Mathematical Reviews number (MathSciNet)
MR3352247

Zentralblatt MATH identifier
1318.53100

#### Citation

Jin, Xin. Holomorphic Lagrangian branes correspond to perverse sheaves. Geom. Topol. 19 (2015), no. 3, 1685--1735. doi:10.2140/gt.2015.19.1685. https://projecteuclid.org/euclid.gt/1510858773

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