Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally convex curves and the Bruhat stratification of the spin group   We study the lifting of the Schubert stratification of the homogeneous space
of complete real flags of $R^{n+1}$ to its universal covering group
$Spin_{n+1}$. We call the lifted strata the Bruhat cells of $Spin_{n+1}$, in
keeping with the homonymous classical decomposition of reductive algebraic
groups. We present explicit parameterizations for these Bruhat cells in terms
of minimal-length expressions $\sigma=a_{i_1}... a_{i_k}$ for permutations
$\sigma\in S_{n+1}$ in terms of the $n$ generators $a_i=(i,i+1)$. These
parameterizations are compatible with the Bruhat orders in the Coxeter-Weyl
group $S_{n+1}$. This stratification is an important tool in the study of
locally convex curves; we present a few such applications.

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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph