6533b7d1fe1ef96bd125d759
RESEARCH PRODUCT
The proof of Birman’s conjecture on singular braid monoids
Luis Parissubject
20F36 57M25. 57M27[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Monoid[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)01 natural sciencesBirman's conjecture[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics - Geometric TopologyMathematics::Group Theory57M25. 57M27Mathematics::Category Theory[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]FOS: MathematicsBraid0101 mathematics[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR][MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]MathematicsConjecturedesingularization010102 general mathematicsMultiplicative functionSigmaGeometric Topology (math.GT)singular braidsInjective function010101 applied mathematicsHomomorphismGeometry and TopologyMathematics - Group Theorydescription
Let B_n be the Artin braid group on n strings with standard generators sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ..., tau_{n-1}. The desingularization map is the multiplicative homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma_i^{+-1}) =_i^{+-1} and eta(tau_i) = sigma_i - sigma_i^{-1}, for 1 <= i <= n-1. The purpose of the present paper is to prove Birman's conjecture, namely, that the desingularization map eta is injective.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-06-30 | Geometry & Topology |