{"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":49034,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"19 4","pages":"679 - 700"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-024-00357-2","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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].
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
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