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arXiv · 1307.5383

Blocked-braid Groups

D. Maglia·N. Sabadini·R. F. C. Walters
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Abstract

We introduce and study a family of groups $\mathbf{BB}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups $\mathbf{B}_n$, and have the corresponding symmetric groups $Σ_n$ as quotients. They are defined by adding a certain class of geometrical modifications to braids. They arise in the study of commutative Frobenius algebras and tangle algebras in braided strict monoidal categories. A fundamental equation true in $\mathbf{BB}_n$ is Dirac's Belt Trick; that torsion through $4π$ is equal to the identity. We show that $\mathbf{BB}_n$ is finite for $n=1,2$ and 3 but infinite for $n>3$.

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D. Maglia, N. Sabadini, R. F. C. Walters. 2013-07-20. Blocked-braid Groups. https://arxiv.org/abs/1307.5383

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