Birman's conjecture for singular braids on closed surfaces

2003/07/17 by Luis Paris, Paris, Luis
Mathematics · #20F36 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F36 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0307233

arxiv created 2003/07/17 · arxiv updated 2009/12/01

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 SB_n(M) be the corresponding singular braid monoid. Our purpose in this paper is to prove that the desingularization map η: SB_n(M) → \Z [B_n(M)], introduced in the definition of the Vassiliev invariants (for braids on surfaces), is injective.

Related

• Presentations for the monoids of singular braids on closed surfaces
• Vassiliev invariants for braids on surfaces
• On the singular braid monoid of an orientable surface
• Automorphisms of surface braid groups
• The braidings in the mapping class groups of surfaces