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math.GT2025
Quantum equations for knots
Thomas Fiedler, Butian Zhang
This paper contains linear systems of equations which can distinguish knots without knot invariants. Let be the topological moduli space of all n-component string links and s…
math.GT2023
Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial
Butian Zhang
A state model for Kauffman polynomial of Dubrovnik-version is given. Based on the state model, the Gauss diagram formulae for Vassiliev invariants are given from the coefficients o…
math.GT2022★ 1 cited
A combinatorial one-cocycle in a moduli space of knots from the Vassiliev invariant of order 3
Baptiste Gros, Butian Zhang
The theory of Gauss diagrams and Gauss diagram formulas provides convenient ways to compute knot invariants, such as coefficients of the HOMFLYPT polynomial. In \cite{4,5}, the aut…