Quantization of the algebra of chord diagrams 453
نویسندگان
چکیده
In this paper we study the algebra L(Σ) generated by links in the manifold Σ¬[0, 1] where Σ is an oriented surface. This algebra has a filtration and the associated graded algebra L Gr (Σ) is naturally a Poisson algebra. There is a Poisson algebra homomorphism from the algebra ch (Σ) of chord diagrams on Σ to L Gr (Σ). We show that multiplication in L (Σ) provides a geometric way to define a deformation quantization of the algebra of chord diagrams on Σ, provided there is a universal Vassiliev invariant for links in Σ¬[0, 1]. If Σ is compact with free fundamental group we construct a universal Vassiliev invariant. The quantization descends to a quantization of the moduli space of flat connections on Σ and it is natural with respect to group homomorphisms.
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