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

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

2010-06-11

arxiv.org/abs/1006.2263v1

Mathematics

Algebraic Topology

Scientific paper

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 $\hind G_{2n}^n=2n-1$.

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