{"title":"Formality of differential graded algebras and complex Lagrangian submanifolds","authors":"Borislav Mladenov","doi":"10.1007/s00029-023-00894-3","DOIUrl":null,"url":null,"abstract":"<p>Let be a compact Kähler Lagrangian in a holomorphic symplectic variety <span>\\(\\textrm{X}/\\textbf{C}\\)</span>. We use deformation quantisation to show that the endomorphism differential graded algebra <span>\\(\\textrm{RHom}\\big (i_*\\textrm{K}_\\textrm{L}^{1/2},i_*\\textrm{K}_\\textrm{L}^{1/2}\\big )\\)</span> is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of <span>\\({\\text {A}}_{\\infty }\\)</span>-modules.\n</p>","PeriodicalId":501600,"journal":{"name":"Selecta Mathematica","volume":"5 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Selecta Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00029-023-00894-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Let be a compact Kähler Lagrangian in a holomorphic symplectic variety \(\textrm{X}/\textbf{C}\). We use deformation quantisation to show that the endomorphism differential graded algebra \(\textrm{RHom}\big (i_*\textrm{K}_\textrm{L}^{1/2},i_*\textrm{K}_\textrm{L}^{1/2}\big )\) is formal. We prove a generalisation to pairs of Lagrangians, along with auxiliary results on the behaviour of formality in families of \({\text {A}}_{\infty }\)-modules.
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