Distinguishing Power of 4-Legendrian Permutation Racks

Source abstract

We study 4-Legendrian racks and their effectiveness at distinguishing Legendrian knots. We prove that the coloring invariant of a permutation rack with a 4-Legendrian rack structure cannot distinguish Legendrian knots that share the same knot type, Thurston–Bennequin number, and rotation number. However, the fundamental 4-Legendrian rack of a Legendrian knot recovers these three classical invariants.