Centralisers in Surface Braid Groups

Abstract

Let Σ be an orientable surface. We generalise Fenn–Rolfsen–Zhu's results on centralisers of singular braids on the disk to singular braids on Σ. As a corollary, we derive a simple and geometric proof of the fact that the word problem is solvable in the monoid of singular braids on n strands on Σ.