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arXiv · 1805.09740

Shrinking braids and Left distributive monoid

Linjun Li
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Abstract

We consider a natural generalization of braids which we call shrinking braids. We state the relations of shrinking braids and use them to define algebraically the monoid $R$. We endow a subset of $R$ with a \emph{left distributive monoid} structure and use it to extend the Dehornoy order on $B_{\infty}$ to an order on $R$. By using this order, we prove that $R$ is isomorphic to the monoid which is generated (geometrically) by shrinking braids.

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Linjun Li. 2018-05-24. Shrinking braids and Left distributive monoid. https://arxiv.org/abs/1805.09740

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