Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fundamental Group of $SO(n)$ Via Quotients of Braid Groups   We describe an algebraic proof of the well-known topological fact that
$\pi_1(SO(n)) \cong Z/2Z$. The fundamental group of $SO(n)$ appears in our
approach as the center of a certain finite group defined by generators and
relations. The latter is a factor group of the braid group $B_n$, obtained by
imposing one additional relation and turns out to be a nontrivial central
extension by $Z/2Z$ of the corresponding group of rotational symmetries of the
hyperoctahedron in dimension $n$.

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The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
21
The categories of this paper are: adap-org