Birman’s conjecture for singular braids on closed surfaces

Abstract

Let M be a closed oriented surface of genus g ≥ 1, let Bn(M) be the braid group of M on n strings, and let SBn(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η : SBn(M) → Z[Bn(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective. AMS Subject Classification: Primary 20F36; Secondary 57M27.

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Cite this paper

@inproceedings{Paris2008BirmansCF, title={Birman’s conjecture for singular braids on closed surfaces}, author={Luis Paris}, year={2008} }