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math.GT2023
Diagram Systems and Generalized Finite Type Theories
Cole Hugelmeyer
We present a category theoretical generalization of the Goussarov theorem for finite type invariants, relating generating sets for generalized finite type theories with diagrams sy…
math.GT2018
A Representation Theorem for Knots and a Generalization of the Fundamental Theorem of Finite Type Invariants
Cole Hugelmeyer
We provide a way to produce knots in from signed chord diagrams, and prove that every knot can be produced in this way. Using these diagrams, we generalize the fundamental th…
math.GT2018
Inscribed Trefoil Knots
Cole Hugelmeyer
Let be a knot type for which the quadratic term of the Conway polynomial is nontrivial, and let be an analytic -periodic function wi…