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.