{"title":"Sheaf quantization and intersection of rational Lagrangian immersions","authors":"Tomohiro Asano, Yuichi Ike","doi":"10.5802/aif.3554","DOIUrl":null,"url":null,"abstract":"We study rational Lagrangian immersions in a cotangent bundle, based on the microlocal theory of sheaves. We construct a sheaf quantization of a rational Lagrangian immersion and investigate its properties in Tamarkin category. Using the sheaf quantization, we give an explicit bound for the displacement energy and a Betti/cup-length estimate for the number of the intersection points of the immersion and its Hamiltonian image by a purely sheaf-theoretic method.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/aif.3554","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
We study rational Lagrangian immersions in a cotangent bundle, based on the microlocal theory of sheaves. We construct a sheaf quantization of a rational Lagrangian immersion and investigate its properties in Tamarkin category. Using the sheaf quantization, we give an explicit bound for the displacement energy and a Betti/cup-length estimate for the number of the intersection points of the immersion and its Hamiltonian image by a purely sheaf-theoretic method.