{"title":"de Rham复合体的扰动","authors":"Ihsane Malass, N. Tarkhanov","doi":"10.17516/1997-1397-2020-13-5-519-532","DOIUrl":null,"url":null,"abstract":"We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is \"small\", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings","PeriodicalId":422202,"journal":{"name":"Journal of Siberian Federal University. Mathematics and Physics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Perturbation of the de Rham Complex\",\"authors\":\"Ihsane Malass, N. Tarkhanov\",\"doi\":\"10.17516/1997-1397-2020-13-5-519-532\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is \\\"small\\\", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings\",\"PeriodicalId\":422202,\"journal\":{\"name\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"volume\":\"19 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Siberian Federal University. Mathematics and Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17516/1997-1397-2020-13-5-519-532\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Siberian Federal University. Mathematics and Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17516/1997-1397-2020-13-5-519-532","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings
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