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arXiv · 2006.08007

A presentation for the planar pure braid group

Jacob Mostovoy
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Abstract

We describe the construction of a minimal presentation for the group of planar pure braids $\overline{P}_n$ on $n$ strands. The generators of this presentation are dual to the generators of the cohomology ring of $\overline{P}_n$ found by Y.Baryshnikov while the relations lie in the commutator subgroup of $\overline{P}_n$. We also construct an explicit (although non-minimal) presentation for the pure cactus group.

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Jacob Mostovoy. 2020-06-14. A presentation for the planar pure braid group. https://arxiv.org/abs/2006.08007

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