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arXiv · 1607.05876

The Fundamental Group of $SO(n)$ Via Quotients of Braid Groups

Ina Hajdini·Orlin Stoytchev
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Abstract

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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Ina Hajdini, Orlin Stoytchev. 2016-07-20. The Fundamental Group of $SO(n)$ Via Quotients of Braid Groups. https://arxiv.org/abs/1607.05876

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