Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $Z_2$-index of the grassmanian $G_{2n}^n$   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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The categories of this paper are: comp-gas
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys