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. [Forum Math., 30 (2018), pp. 1539–1572]. [ABSTRACT FROM AUTHOR]