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arXiv · 1006.2263

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

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

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BibTeXRIS

R. N. Karasev. 2010-06-11. $Z_2$-index of the grassmanian $G_{2n}^n$. https://arxiv.org/abs/1006.2263

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