The proof of Birman's conjecture on singular braid monoids
Paris, Luis
HAL, hal-00128156 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 
@article{hal-00128156,
     author = {Paris, Luis},
     title = {The proof of Birman's conjecture on singular braid monoids},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00128156}
}

Paris, Luis. The proof of Birman's conjecture on singular braid monoids. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00128156/