Shrinking braids and Left distributive monoid

2018/05/24 by Linjun Li, Li, Linjun
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1805.09740

openalex publication_date 2018/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_∞ 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.

Related

• The well-ordering of dual braid monoids
• Left-Garside categories, self-distributivity, and braids
• Alternating normal forms for braids and locally Garside monoids
• Monoid and group of pseudo braids
• Presentations for the monoids of singular braids on closed surfaces