Holomorphic Lagrangian branes correspond to perverse sheaves

Abstract

Let X be a compact complex manifold, $D_c^b(X)$ be the bounded derived category of constructible sheaves on $X$, and $Fuk(T^{\ast }X)$ be the Fukaya category of $T^{\ast }X$. A Lagrangian brane in $Fuk(T^{\ast }X)$ is holomorphic if the underlying Lagrangian submanifold is complex analytic in $T^{\ast }{X}_{\mathbb{C}}$, the holomorphic cotangent bundle of $X$. We prove that under the quasi-equivalence between $D_c^b(X)$ and $DFuk(T^{\ast }X)$ established in [NaZa09] and [Nad09], holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.

Significant improvement of the previous version. Comments are welcome!

References in corpus (3)

• A-branes and Noncommutative Geometry
• Holomorphic Lagrangian branes correspond to perverse sheaves
• Floer cohomology of real Lagrangians in the Fermat quintic threefold

Cited by in corpus (8)

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• Holomorphic Lagrangian branes correspond to perverse sheaves
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• Homological mirror symmetry for hypertoric varieties II (with an Appendix written jointly with Laurent Côté and Justin Hilburn)
• Symplectomorphism group of $T^{\ast }(G_{\mathbb{C}}/B)$ and the braid group I: a homotopy equivalence for $G_{\mathbb{C}}=S{L}_3(\mathbb{C})$
• Homological Mirror Symmetry for the universal centralizers I: The adjoint group case