# Birman's conjecture for singular braids on closed surfaces

Abstract : Let $M$ be a closed oriented surface of genus $g\ge 1$, let $B_n(M)$ be the braid group of $M$ on $n$ strings, and let $SB_n(M)$ 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.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00128178
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Submitted on : Wednesday, January 31, 2007 - 9:55:46 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM

### Citation

Luis Paris. Birman's conjecture for singular braids on closed surfaces. Journal of Knot Theory and its Ramification, 2004, 13, pp.895-915. ⟨hal-00128178⟩

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