Formality of differential graded algebras and complex Lagrangian submanifolds

Abstract

Let $i:\mathrm{L}\hookrightarrow \mathrm{X}$ be a compact Kähler Lagrangian in a holomorphic symplectic variety $\mathrm{X}/\mathbf{C}$. We use deformation quantisation to show that the endomorphism differential graded algebra $\mathrm{RHom}(i_{\ast }{\mathrm{K}}_{\mathrm{L}}^{1/2},i_{\ast }{\mathrm{K}}_{\mathrm{L}}^{1/2})$ is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of ${\mathrm{A}}_{\infty }$-modules.

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References in corpus (4)

• Categorification of Lagrangian intersections on complex symplectic manifolds using perverse sheaves of vanishing cycles
• Stacks of quantization-deformation modules on complex symplectic manifolds
• Locality in the Fukaya category of a hyperkähler manifold
• Degeneration of spectral sequences and complex Lagrangian submanifolds

Cited by in corpus (1)

• Degeneration of spectral sequences and complex Lagrangian submanifolds