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arXiv · 1508.03699

On the structure of braid groups on complexes

Byung Hee An·Hyo Won Park
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Abstract

We consider the braid groups $\mathbf{B}_n(X)$ on finite simplicial complexes $X$, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for $X$ and their effects on braid groups, and provide an algorithmic way to compute the group presentations for $\mathbf{B}_n(X)$ with the aid of them. As applications, we give complete criteria for both the surface embeddability and planarity for $X$, which are the torsion-freeness of the braid group $\mathbf{B}_n(X)$ and its abelianization $H_1(\mathbf{B}_n(X))$, respectively.

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BibTeXRIS

Byung Hee An, Hyo Won Park. 2015-08-15. On the structure of braid groups on complexes. https://doi.org/10.1016/j.topol.2017.05.001

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