The $\mathbb {Z}/2$ Fadell–Husseini index of the complex Grassmann manifolds $G_{n}(\mathbb {C}^{2n})$

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2024年10月22日

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Arijit Nath,
Avijit Nath

摘要

In this paper, we study the $\mathbb {Z}/2$ $Z / 2$ action on complex Grassmann manifolds $G_{n}(\mathbb {C}^{2n})$ $G_{n} (C^{2 n})$ given by taking orthogonal complement. We completely compute the associated $\mathbb {Z}/2$ $Z / 2$ Fadell–Husseini index. Our study is parallel to the study of the index of real Grassmann manifolds $G_n(\mathbb {R}^{2n})$ $G_{n} (R^{2 n})$ by Baralić et al. [Forum Math., 30 (2018), pp. 1539–1572].

The \(\mathbb {Z}/2\) Fadell–Husseini index of the complex Grassmann manifolds \(G_{n}(\mathbb {C}^{2n})\)

摘要