Birman's conjecture for singular braids on closed surfaces
Abstract
Let
M
be a closed oriented surface of genus
g≥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 $\eta: SB_n(M) \to \Z [B_n(M)]$, introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective.