5 papers
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…
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…
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…
The Hilden Double Coset Problem in Braid Groups
Seth Hovland
In this paper we provide a solution to the double coset problem for the braid group modulo the Hilden subgroup This result demonstrates that, as in the case of braid c…
The Restriction of Efficient Geodesics to the Non-separating Complex of Curves
Seth Hovland, Greg Vinal
In the complex of curves of a closed orientable surface of genus a preferred finite set of geodesics between any two vertices, called \emph{efficient geode…