Kontsevich integral for knots and Vassiliev invariants

Abstract

We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented.

25 pages, 17 figures

References in corpus (1)

• Chern-Simons Theory in the Temporal Gauge and Knot Invariants through the Universal Quantum R-Matrix

Cited by in corpus (18)

• Colored HOMFLY polynomials for the pretzel knots and links
• Introduction to Khovanov Homologies. III. A new and simple tensor-algebra construction of Khovanov-Rozansky invariants
• Towards effective topological field theory for knots
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• On 3d extensions of AGT relation
• Genus expansion of HOMFLY polynomials
• On genus expansion of superpolynomials
• Racah matrices and hidden integrability in evolution of knots
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Quantum Racah matrices and 3-strand braids in irreps R with |R|=4
• Colored Alexander polynomials and KP hierarchy
• Gaussian distribution of LMOV numbers
• A new symmetry of the colored Alexander polynomial
• Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure
• Vassiliev invariants for pretzel knots
• Vogel's universality and the classification problem for Jacobi identities
• Algebraic structures of Vassiliev invariants for knot families
• On ambiguity in knot polynomials for virtual knots