{"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":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"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\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2024-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00682-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00682-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","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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