Singular braids and partial permutations

James East

Abstract

We introduce and study the partial singular braid monoid \(\mathcal{PSB}_n\), a monoid that contains both the inverse braid monoid \(\mathcal{IB}_n\) and the singular braid monoid \(\mathcal{SB}_n\). Our main results include a characterization of Green's relations, a presentation in terms of generators and relations, and a proof that \(\mathcal{PSB}_n\) embeds in the semigroup algebra \(\mathbb C[\mathcal{IB}_n]\).

Keywords: Braids, Singular braid monoids, Inverse braid monoids, Presentations, Birman's conjecture.

AMS Subject Classification: Primary 20F36;; secondary 20M05.