$Z_2$-index of the grassmanian $G_{2n}^n$

Abstract

We study the real Grassmann manifold $G_{2n}^n$ (of $n$-subspaces in ${\mathbb{R}}^{2n}$), and the action of $Z_2$ on it by taking the orthogonal complement. The homological index of this action is estimated from above and from below. In case $n$ is a power of two it is shown that $\hind G_{2n}^n=2n-1$.

References in corpus (1)

• Topological transversals to a family of convex sets