{"title":"一般的Cartan模型","authors":"L. Tu","doi":"10.2307/j.ctvrdf1gz.27","DOIUrl":null,"url":null,"abstract":"This chapter looks at the Cartan model. Specifically, it generalizes the Cartan model from a circle action to a connected Lie group action. The chapter assumes the Lie group to be connected, because the condition that LX α = 0 is sufficient for a differential form α on M to be invariant holds only for a connected Lie group. It also considers the theorem that marks the transition from the Weil model to the Cartan model. It is due to Henri Cartan, who played a crucial role in the development of equivariant cohomology. The chapter then studies the Weil-Cartan isomorphism.","PeriodicalId":272846,"journal":{"name":"Introductory Lectures on Equivariant Cohomology","volume":"54 8-9","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Cartan Model in General\",\"authors\":\"L. Tu\",\"doi\":\"10.2307/j.ctvrdf1gz.27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This chapter looks at the Cartan model. Specifically, it generalizes the Cartan model from a circle action to a connected Lie group action. The chapter assumes the Lie group to be connected, because the condition that LX α = 0 is sufficient for a differential form α on M to be invariant holds only for a connected Lie group. It also considers the theorem that marks the transition from the Weil model to the Cartan model. It is due to Henri Cartan, who played a crucial role in the development of equivariant cohomology. The chapter then studies the Weil-Cartan isomorphism.\",\"PeriodicalId\":272846,\"journal\":{\"name\":\"Introductory Lectures on Equivariant Cohomology\",\"volume\":\"54 8-9\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Introductory Lectures on Equivariant Cohomology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2307/j.ctvrdf1gz.27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Introductory Lectures on Equivariant Cohomology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2307/j.ctvrdf1gz.27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This chapter looks at the Cartan model. Specifically, it generalizes the Cartan model from a circle action to a connected Lie group action. The chapter assumes the Lie group to be connected, because the condition that LX α = 0 is sufficient for a differential form α on M to be invariant holds only for a connected Lie group. It also considers the theorem that marks the transition from the Weil model to the Cartan model. It is due to Henri Cartan, who played a crucial role in the development of equivariant cohomology. The chapter then studies the Weil-Cartan isomorphism.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
