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arXiv · 1909.10962

The root extraction problem for generic braids

María Cumplido·Juan González-Meneses·Marithania Silvero
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Abstract

We show that, generically, finding the $k$-th root of a braid is very fast. More precisely, we provide an algorithm which, given a braid $x$ on $n$ strands and canonical length $l$, and an integer $k>1$, computes a $k$-th root of $x$, if it exists, or guarantees that such a root does not exist. The generic-case complexity of this algorithm is $O(l(l+n)n^3\log n)$. The non-generic cases are treated using a previously known algorithm by Sang-Jin Lee.

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María Cumplido, Juan González-Meneses, Marithania Silvero. 2019-09-24. The root extraction problem for generic braids. https://arxiv.org/abs/1909.10962

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