Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 2-ranks of connected compact Lie groups   The 2-rank of a compact Lie group $G$ is the maximal possible rank of the
elementary 2-subgroup ${\mathbb Z}_{2}\times... {\mathbb Z}_{2}$ of $G$. The
study of 2-ranks (and $p$-rank for any prime $p$) of compact Lie groups was
initiated in 1953 by A. Borel and J.-P. Serre. Since then the 2-ranks of
compact Lie groups have been investigated by many mathematician. The 2-ranks of
compact Lie groups relate closely with several important areas in mathematics.
  In this article, we survey important results concerning 2-ranks of compact
Lie groups. In particular, we present the complete determination of 2-ranks of
compact connected simple Lie groups $G$ via the 2-numbers introduced by B. Y.
Chen and T. Nagano in [Un invariant g\'em\'etrique riemannien, C. R. Acad. Sci.
Paris, 295 (1982), 389--391] and [A Riemannian geometric invariant and its
applications to a problem of Borel and Serre, Trans. Amer. Math. Soc. 308
(1988), 273--297].

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: cs