6533b837fe1ef96bd12a280b

RESEARCH PRODUCT

Birman's conjecture for singular braids on closed surfaces

Luis Paris

subject

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]MonoidPure mathematics[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]Mathematics - Geometric TopologyMathematics::Group Theory[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]Mathematics::Category TheoryMathematics::Quantum AlgebraGenus (mathematics)0103 physical sciencesFOS: MathematicsBraid0101 mathematicsMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]Algebra and Number TheoryConjecture010102 general mathematicsGeometric Topology (math.GT)20F36;57M27Braid theorySurface (topology)Mathematics::Geometric TopologyInjective function57M27010307 mathematical physicsMathematics - Group Theory

description

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.

yearjournalcountryeditionlanguage
2003-07-17
https://hal.science/hal-00128178