The proof of Birman's conjecture on singular braid monoids
Luis Paris
Abstract
Let Bn be the Artin braid group on n strings with standard generators sigma1, ..., sigman-1, and let SBn be the singular braid monoid with generators sigma1+-1, ..., sigman-1+-1, tau1, ..., taun-1. The desingularization map is the multiplicative homomorphism eta: SBn --> Z[Bn] defined by eta(sigmai+-1) =i+-1 and eta(taui) = sigmai - sigmai-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.
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