Configuration Space Integrals and Universal Vassiliev Invariants over Closed Surfaces
We show the existence of a universal Vassiliev invariant for links in closed surface cylinders by explicit construction using configuration space integrals.
q-alg↗
arXiv subjects
Josef Mattes
Publications and source records attributed to Josef Mattes.
Quantization of the Algebra of Chord Diagrams
In this paper we define an algebra structure on the vector space $L(Σ)$ generated by links in the manifold $Σ\times [0,1]$ 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 of chord diagrams $ch(Σ)$ 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, provided there is a universal Vassiliev invariant for links in $Σ\times [0,1]$. The quantization descends to a quantization of the moduli space of flat connections on $Σ$ and it is universal with respect to group homomorphisms. If $Σ$ is compact with free fundamental group we construct a universal Vassiliev invariant.
q-alg↗