{"title":"各向同性环面作用的等变形式","authors":"Jeffrey D. Carlson","doi":"10.1007/s40062-018-0207-5","DOIUrl":null,"url":null,"abstract":"<p>Considering the potential equivariant formality of the left action of a connected Lie group <i>K</i> on the homogeneous space <i>G</i>?/?<i>K</i>, we arrive through a sequence of reductions at the case <i>G</i> is compact and simply-connected and <i>K</i> is a torus. We then classify all pairs (<i>G</i>,?<i>S</i>) such that <i>G</i> is compact connected Lie and the embedded circular subgroup <i>S</i> acts equivariantly formally on <i>G</i>?/?<i>S</i>. In the process we provide what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-018-0207-5","citationCount":"7","resultStr":"{\"title\":\"Equivariant formality of isotropic torus actions\",\"authors\":\"Jeffrey D. Carlson\",\"doi\":\"10.1007/s40062-018-0207-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Considering the potential equivariant formality of the left action of a connected Lie group <i>K</i> on the homogeneous space <i>G</i>?/?<i>K</i>, we arrive through a sequence of reductions at the case <i>G</i> is compact and simply-connected and <i>K</i> is a torus. We then classify all pairs (<i>G</i>,?<i>S</i>) such that <i>G</i> is compact connected Lie and the embedded circular subgroup <i>S</i> acts equivariantly formally on <i>G</i>?/?<i>S</i>. In the process we provide what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s40062-018-0207-5\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-018-0207-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-018-0207-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Considering the potential equivariant formality of the left action of a connected Lie group K on the homogeneous space G?/?K, we arrive through a sequence of reductions at the case G is compact and simply-connected and K is a torus. We then classify all pairs (G,?S) such that G is compact connected Lie and the embedded circular subgroup S acts equivariantly formally on G?/?S. In the process we provide what seems to be the first published proof of the structure (known to Leray and Koszul) of the cohomology rings
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