Distinguishing Power of 4-Legendrian Permutation Racks

Abstract

We study 4-Legendrian racks and their effectiveness at distinguishing Legendrian knots. We prove that permutation racks with 4-Legendrian rack structures cannot distinguish Legendrian knots that share the same knot type, Thurston-Bennequin number, and rotation number. However, they also recover these three classical invariants.

14 pages, 4 figures, 1 table