Geometry & Topology

Holomorphic Lagrangian branes correspond to perverse sheaves

Xin Jin

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

Article information

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

Received: 29 March 2014
Revised: 18 July 2014
Accepted: 16 August 2014
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D40: Floer homology and cohomology, symplectic aspects 32S60: Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]

Fukaya category holomorphic Lagrangian branes perverse sheaves constructible sheaves Nadler–Zaslow correspondence


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

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