Birman's conjecture is true for I2(p)

In 1993, Birman conjectured that the desingularization map from the singular braid monoid to the integral group ring of the braid group determined by $\\sigma_i^{\\pm1}\\mapsto\\sigma_i^{\\pm1}$ and $\\tau_i\\mapsto\\sigma_i-\\sigma_i^{-1}$ is injective. The conjecture, which has recently been proven true by Paris (2004), may be generalized to all Artin groups. In this article we prove that the generalized conjecture holds for one of the infinite families of Artin groups of spherical type, namely I2(p).