Combinatorial expression for universal Vassiliev link invariant

TL;DR

This paper introduces a combinatorial state sum model that generates all R-matrix type link invariants and universal Vassiliev invariants, simplifying previous integral-based formulations like Kontsevich's.

Contribution

It presents a new combinatorial expression for the universal Vassiliev link invariant that is simpler than Kontsevich's integral-based approach.

Findings

Constructed a general R-matrix type state sum model for link invariants

Model encompasses all R-matrix invariants and universal Vassiliev invariants

Simplifies previous integral-based formulas by avoiding integrals except for the associator

Abstract

The most general R-matrix type state sum model for link invariants is constructed. It contains in itself all R-matrix invariants and is a generating function for "universal" Vassiliev link invariants. This expression is more simple than Kontsevich's expression for the same quantity, because it is defined combinatorially and does not contain any integrals, except for an expression for "the universal Drinfeld's associator".