Formality of differential graded algebras and complex Lagrangian submanifolds

2020/07/10 by Mladenov, Borislav
#14F40 (Secondary) #14J42 #16E45 #53D12 #53D55 (Primary) 18G40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2007.05498

Abstract

Let i: L \hookrightarrow X be a compact Kähler Lagrangian in a holomorphic symplectic variety X/C. We use deformation quantisation to show that the endomorphism differential graded algebra RHom(i_*K_L^1/2,i_*K_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 A_∞-modules.

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