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.

[1]  D. Thurston.  Integral Expressions for the Vassiliev Knot Invariants , 1999, math/9901110.

[2]  N. Reshetikhin,et al.  Quantization of the algebra of chord diagrams , 1997, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  J. Dubochet,et al.  Geometry and physics of knots , 1996, Nature.

[4]  W. Kazez.  Non-associative tangles , 1996 .

[5]  N. Reshetikhin,et al.  The poisson structure on the moduli space of flat connections and chord diagrams , 1996 .

[6]  D. Altschuler,et al.  Vassiliev Knot Invariants and Chern-Simons Perturbation Theory to All Orders , 1996, q-alg/9603010.

[7]  D. Bar-Natan.  PERTURBATIVE CHERN-SIMONS THEORY , 1995 .

[8]  Dror Bar-Natan,et al.  On the Vassiliev knot invariants , 1995 .

[9]  Raoul Bott,et al.  On the self‐linking of knots , 1994 .

[10]  A. Alekseev,et al.  Combinatorial quantization of the Hamiltonian Chern-Simons theory I , 1994, hep-th/9403066.

[11]  Le Tu Quoc Thang,et al.  The universal Vassiliev-Kontsevich invariant for framed oriented links , 1994, hep-th/9401016.

[12]  M. Kontsevich.  Vassiliev’s knot invariants , 1993 .

[13]  I. Singer,et al.  Chern-Simons perturbation theory. II , 1993, hep-th/9304087.

[14]  I. Singer,et al.  Chern-Simons Perturbation Theory , 1991, hep-th/9110056.

[15]  S. D. Pietra,et al.  Geometric quantization of Chern-Simons gauge theory , 1991 .

[16]  Victor A. Vassiliev,et al.  Cohomology of knot spaces , 1990 .

[17]  N. Hitchin.  Flat connections and geometric quantization , 1990 .

[18]  M. Martellini,et al.  Wilson lines in Chern-Simons theory and link invariants , 1990 .

[19]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[20]  J. Mattes.  Functions on the moduli space of flat $G , 1997 .

[21]  Ntón,et al.  Quantum Moduli Spaces of Flat Connections , 1996 .

[22]  D. Bar-Natan.  NON-ASSOCIATIVE TANGLES , 1995 .

[23]  W. Fulton,et al.  A compactification of configuration spaces , 1994 .

[24]  Victor Pavlovich Maslov,et al.  Advances in Soviet mathematics , 1990 .