Birman's conjecture for singular braids on closed surfaces

Luis Paris

Birman's conjecture for singular braids on closed surfaces

Geometric Topology 2007-05-23 v1 Group Theory

Authors: Luis Paris

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.

Keywords

braid groups

Cite

@article{arxiv.math/0307233,
  title  = {Birman's conjecture for singular braids on closed surfaces},
  author = {Luis Paris},
  journal= {arXiv preprint arXiv:math/0307233},
  year   = {2007}
}

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