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arXiv · 0906.0137

Complexity of relations in the braid group

Joel Hass·Arkadius Kalka·Tahl Nowik
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Abstract

We show that for any given n, there exists a sequence of words a_k in the generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the identity element of B_n, such that the number of braid relations of the form sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass from a_k to the empty word is quadratic with respect to the length of a_k.

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Joel Hass, Arkadius Kalka, Tahl Nowik. 2009-05-31. Complexity of relations in the braid group. https://arxiv.org/abs/0906.0137

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