3 papers
math.GT2026
Every Plat Presentation Admits a Positive Bounded Braid Representative
Seth Hovland
Classifying link types via their n-bridge positions requires navigating vast Hilden double coset classes H2n\B2n/H2n. We provide a restriction on this by proving that every Hilden…
math.GT2024
Bridge Positions and Plat Presentations of Links
Seth Hovland
This paper investigates the relationship between links in bridge position and plat presentations. We prove that Hilden double coset classes of plat presentations correspond exactly…
math.GT2024
Generating Infinitely Many Hyperbolic Knots with Plats
Carolyn Engelhardt, Seth Hovland
In this paper we study the relationships between links in plat position, the dynamics of the braid group, and Heegaard splittings of double branched covers of over a link. Th…