{"title":"复格拉斯曼流形 \\(G_{n}(\\mathbb {C}^{2n})\\) 的 Fadell-Husseini 指数","authors":"Arijit Nath, Avijit Nath","doi":"10.1007/s40062-024-00357-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the <span>\\(\\mathbb {Z}/2\\)</span> action on complex Grassmann manifolds <span>\\(G_{n}(\\mathbb {C}^{2n})\\)</span> given by taking orthogonal complement. We completely compute the associated <span>\\(\\mathbb {Z}/2\\)</span> Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds <span>\\(G_n(\\mathbb {R}^{2n})\\)</span> by Baralić et al. [Forum Math., <b>30</b> (2018), pp. 1539–1572].</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The \\\\(\\\\mathbb {Z}/2\\\\) Fadell–Husseini index of the complex Grassmann manifolds \\\\(G_{n}(\\\\mathbb {C}^{2n})\\\\)\",\"authors\":\"Arijit Nath, Avijit Nath\",\"doi\":\"10.1007/s40062-024-00357-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study the <span>\\\\(\\\\mathbb {Z}/2\\\\)</span> action on complex Grassmann manifolds <span>\\\\(G_{n}(\\\\mathbb {C}^{2n})\\\\)</span> given by taking orthogonal complement. We completely compute the associated <span>\\\\(\\\\mathbb {Z}/2\\\\)</span> Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds <span>\\\\(G_n(\\\\mathbb {R}^{2n})\\\\)</span> by Baralić et al. [Forum Math., <b>30</b> (2018), pp. 1539–1572].</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40062-024-00357-2\",\"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/s40062-024-00357-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The \(\mathbb {Z}/2\) Fadell–Husseini index of the complex Grassmann manifolds \(G_{n}(\mathbb {C}^{2n})\)
In this paper, we study the \(\mathbb {Z}/2\) action on complex Grassmann manifolds \(G_{n}(\mathbb {C}^{2n})\) given by taking orthogonal complement. We completely compute the associated \(\mathbb {Z}/2\) Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds \(G_n(\mathbb {R}^{2n})\) by Baralić et al. [Forum Math., 30 (2018), pp. 1539–1572].
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