Distinguishing Power of 4-Legendrian Permutation Racks
Published: Oct 30, 2025
Last Updated: Oct 30, 2025
Authors:Luc Ta, Peyton Phinehas Wood
Abstract
We explore 4-Legendrian rack structures and the effectiveness of 4-Legendrian racks to distinguish Legendrian knots. We prove that permutation racks with a 4-Legendrain rack structure cannot distinguish sets of Legendrian knots with the same knot type, Thurston-Bennequin number, and rotation number.