Research ArticleNo Access

Shrinking braids and left distributive monoid

Tsinghua University, 100084 Beijing, P. R. China

Present Address: Department of Mathematics, University of Pennsylvania, Philadelphia, PA.

https://doi.org/10.1142/S0218216521500279Cited by:0 (Source: Crossref)

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 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.

Keywords:

AMSC: 03C05, 06F05, 20M30

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