Birman's conjecture for singular braids on closed surfaces

Luis Paris

paper

Birman's conjecture for singular braids on closed surfaces

arXiv:math/0307233

Abstract

Let $M$ be a closed oriented surface of genus $g \geq 1$ , let $B_{n} (M)$ be the braid group of $M$ on $n$ strings, and let $S B_{n} (M)$ be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map $η : S B_{n} (M) \to Z [B_{n} (M)]$ , introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective.