{"title":"剪切的奇异支持是 γ-各向异性的","authors":"Stéphane Guillermou, Claude Viterbo","doi":"10.1007/s00039-024-00682-x","DOIUrl":null,"url":null,"abstract":"<p>We prove that the singular support of an element in the derived category of sheaves is <i>γ</i>-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being <i>γ</i>-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by <i>C</i><sup>1</sup> diffeomorphisms) and we give an example of an involutive set that is not <i>γ</i>-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm <i>γ</i> and raise a number of new questions.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":"30 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Singular Support of Sheaves Is γ-Coisotropic\",\"authors\":\"Stéphane Guillermou, Claude Viterbo\",\"doi\":\"10.1007/s00039-024-00682-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that the singular support of an element in the derived category of sheaves is <i>γ</i>-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being <i>γ</i>-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by <i>C</i><sup>1</sup> diffeomorphisms) and we give an example of an involutive set that is not <i>γ</i>-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm <i>γ</i> and raise a number of new questions.</p>\",\"PeriodicalId\":12478,\"journal\":{\"name\":\"Geometric and Functional Analysis\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometric and Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00682-x\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometric and Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00682-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove that the singular support of an element in the derived category of sheaves is γ-coisotropic, a notion defined in [Vit22]. We prove that this implies that it is involutive in the sense of Kashiwara-Schapira, but being γ-coisotropic has the advantage to be invariant by symplectic homeomorphisms (while involutivity is only invariant by C1 diffeomorphisms) and we give an example of an involutive set that is not γ-coisotropic. Along the way we prove a number of results relating the singular support and the spectral norm γ and raise a number of new questions.
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Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis.
GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016.
Publishes major results on topics in geometry and analysis.
Features papers which make connections between relevant fields and their applications to other areas.
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