TheZ/2Fadell–Husseini index of the complex Grassmann manifoldsGn(C2n)

In this paper, we study the Z / 2 action on complex Grassmann manifolds G n ( C 2 n ) given by taking orthogonal complement. We completely compute the associated Z / 2 Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds G n ( R 2 n ) by Baralić et al. [...

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Bibliographic Details
Published inJournal of homotopy and related structures Vol. 19; no. 4; pp. 679 - 700
Main Authors Nath, Arijit, Nath, Avijit
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2024
Subjects
Algebra
Algebraic Topology
Functional Analysis
Mathematics
Mathematics and Statistics
Number Theory
55N91
Secondary 55M35
Complex Grassmann manifolds
Fadell–Husseini index
Equivariant cohomology
Existence of equivariant maps
Primary 51F25
55M20
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Summary:In this paper, we study the Z / 2 action on complex Grassmann manifolds G n ( C 2 n ) given by taking orthogonal complement. We completely compute the associated Z / 2 Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds G n ( R 2 n ) by Baralić et al. [Forum Math., 30 (2018), pp. 1539–1572].
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-024-00357-2