Cole Hugelmeyer

collaborators

3 papers

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 $S^{3}$ 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 $K$ be a knot type for which the quadratic term of the Conway polynomial is nontrivial, and let $γ : R \to R^{3}$ be an analytic $Z$ -periodic function wi…

math.MG2018

Every smooth Jordan curve has an inscribed rectangle with aspect ratio equal to $3$

Cole Hugelmeyer

We use Batson's lower bound on the nonorientable slice genus of $(2 n, 2 n - 1)$ -torus knots to prove that for any $n \geq 2$ , every smooth Jordan curve has an inscribed rectangle of of…

A Representation Theorem for Knots and a Generalization of the Fundamental Theorem of Finite Type Invariants

Inscribed Trefoil Knots

Every smooth Jordan curve has an inscribed rectangle with aspect ratio equal to 3​

Every smooth Jordan curve has an inscribed rectangle with aspect ratio equal to $3$