Formality of differential graded algebras and complex Lagrangian submanifolds

Abstract

Let be a compact Kähler Lagrangian in a holomorphic symplectic variety X/C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{X}/\ extbf{C}$$\\end{document}. We use deformation quantisation to show that the endomorphism differential graded algebra RHom(i∗KL1/2,i∗KL1/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{RHom}\\big (i_*\ extrm{K}_\ extrm{L}^{1/2},i_*\ extrm{K}_\ extrm{L}^{1/2}\\big )$$\\end{document} is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of A∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ext {A}}_{\\infty }$$\\end{document}-modules.