{"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}
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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.
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