On minimal crossing number braid diagrams and homogeneous braids

Ilya Alekseev; Geidar Mamedov

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arXiv · 1905.03210

On minimal crossing number braid diagrams and homogeneous braids

Ilya Alekseev·Geidar Mamedov

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Abstract

We study braid diagrams with a minimal number of crossings. Such braid diagrams correspond to geodesic words for the braid groups with standard Artin generators. We prove that a diagram of a homogeneous braid is minimal if and only if it is homogeneous. We conjecture that monoids of homogeneous braids are Artin-Tits monoids and prove that monoids of alternating braids are right-angled Artin monoids. Using this, we give a lower bound on the growth rate of the braid groups.

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Ilya Alekseev, Geidar Mamedov. 2019-05-08. On minimal crossing number braid diagrams and homogeneous braids. https://arxiv.org/abs/1905.03210

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