Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second homotopy and invariant geometry of flag manifolds   We use the Hopf fibration to explicitly compute generators of the second
homotopy group of the flag manifolds of a compact Lie group. We show that these
$2$-spheres have nice geometrical properties such as being totally geodesic
surfaces with respect to any invariant metric on the flag manifold. We
characterize when the generators with the same invariant geometry are in the
same homotopy class. This is done by exploring the action of Weyl group on the
irreducible components of isotropy representation of the flag manifold.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph