The braid group $B_3$ in the framework of continued fractions

Amitesh Datta

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arXiv · 2008.02262

The braid group $B_3$ in the framework of continued fractions

Amitesh Datta

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Abstract

We use the classical interpretation of the braid group $B_3$ as a central extension of the modular group $\text{PSL}_2\left(\mathbb{Z}\right)$ to establish new and fundamental properties of $B_3$ using the theory of continued fractions. In particular, we give simple and natural linear time algorithms to solve the word and conjugacy problems in $B_3$. The algorithms introduced in this paper are easy to implement and are the most efficient algorithms in the literature to solve these problems in the braid group $B_3$.

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BibTeX RIS

Amitesh Datta. 2020-08-05. The braid group $B_3$ in the framework of continued fractions. https://arxiv.org/abs/2008.02262

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