3 citations · 3 across the 3 of their papers we have counts for
5 papers
Hexagonal lattice diagrams for complex curves in
Alexander Zupan
We demonstrate that the geometric, topological, and combinatorial complexities of certain surfaces in are closely related: We prove that a positive genus surface $\…
Equivalent characterizations of handle-ribbon knots
Maggie Miller, Alexander Zupan
The stable Kauffman conjecture posits that a knot in is slice if and only if it admits a slice derivative. We prove a related statement: A knot is handle-ribbon (also called…
The Powell Conjecture and reducing sphere complexes
Alexander Zupan
The Powell Conjecture offers a finite generating set for the genus Goeritz group, the group of automorphisms of that preserve a genus Heegaard surface , generali…
Bridge spectra of iterated torus knots
Alexander Zupan
We determine the set of all genus g bridge numbers of many iterated torus knots, listing these numbers in a sequence called the bridge spectrum. In addition, we prove a structural…
Properties of knots preserved by cabling
Alexander Zupan
We examine geometric properties of a knot J that are unchanged by taking a (p,q)-cable K of J. Specifically, we relate w(K) to w(J), where w(K) is the width of K in the sense of Ga…