## 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.

: Primary 20F36;; secondary 20M05.

This paper is available as a pdf (220kB) file.

 Thursday, January 14, 2010