Addendum to “On some torus knot groups and submonoids of the braid groups” [J. Algebra 607 (Part B) (2022) 260–289

Abstract

In [3], we gave a conjectural presentation of the submonoid of the (n+1)-strand braid group Bn+1 (n≥3) generated by σ1,σ1σ2,…,σ1σ2⋯σn, generalizing a conjecture given by Dehornoy for n=3. We show that this conjecture is false for all n≥3, by showing that the presentation which we exhibited defines a monoid which is not left-cancellative.