The proof of Birman’s conjecture on singular braid monoids
نویسنده
چکیده
Let Bn be the Artin braid group on n strings with standard generators σ1, . . . , σn−1 , and let SBn be the singular braid monoid with generators σ ±1 1 , . . . , σ ±1 n−1, τ1, . . . , τn−1 . The desingularization map is the multiplicative homomorphism η : SBn → Z[Bn] defined by η(σ ±1 i ) = σ ±1 i and η(τi) = σi − σ −1 i , for 1 ≤ i ≤ n − 1. The purpose of the present paper is to prove Birman’s conjecture, namely, that the desingularization map η is injective. AMS Classification numbers Primary: 20F36 Secondary: 57M25. 57M27
منابع مشابه
Birman’s conjecture for singular braids on closed surfaces
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. AMS Subject Classification: Primary 20F36; Seconda...
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