Orthogonal shadows and index of Grassmann manifolds

Djordje Baralić, Pavle V. M. Blagojević, Roman Karasev +1

In this paper we study the $\mathbb{Z}/2$ action on real Grassmann manifolds $G_n({\mathbb{R}}^{2n})$ and ${\tilde{G}}_n({\mathbb{R}}^{2n})$ given by taking (appropriately oriented) orthogonal complemen…