Year: 2026
Type: article
Abstract: 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 to bridge positions of a link up to bridge isotopy. This correspondence allows us to translate algebraic questions about plat presentations into geometric questions about bridge positions. Using this perspective, we re-establish several results from both frameworks. In particular, we show that there is a unique Hilden double coset class for the n-bridge unknot in S 3 , and that torus knots admit a single double coset class in plat position. Finally, we discuss how this correspondence can be used to study plat closures of braids, which is the subject of ongoing research.
Author: Seth Hovland
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404342355