## Holomorphic Lagrangian branes correspond to perverse sheaves.(English)Zbl 1318.53100

Summary: Let $$X$$ be a compact complex manifold, $$D_c^b(X)$$ be the bounded derived category of constructible sheaves on $$X$$, and $$\mathrm{Fuk}(T^*X)$$ be the Fukaya category of $$T^*X$$. A Lagrangian brane in $$\mathrm{Fuk}(T^*X)$$ is holomorphic if the underlying Lagrangian submanifold is complex analytic in $$T^*X_{\mathbb{C}}$$, the holomorphic cotangent bundle of $$X$$. We prove that under the quasiequivalence between $$D^b_c(X)$$ and $$\mathrm{DFuk}(T^*X)$$ established by Nadler and Zaslow, holomorphic Lagrangian branes with appropriate grading correspond to perverse sheaves.

### MSC:

 53D40 Symplectic aspects of Floer homology and cohomology 32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
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### References:

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