Commun. Korean Math. Soc. Published online March 18, 2021
Jose Ceniceros, Mohamed Elhamdadi, and Sam Nelson
Hamilton College, University of South Florida, Claremont McKenna College
Abstract : We define a new algebraic structure called Legendrian racks or racks with Legendrian structure, motivated by the front-projection Reidemeister moves for Legendrian knots. We provide examples of Legendrian racks and use these algebraic structures to define invariants of Legendrian knots with explicit computational examples. We classify Legendrian structures on racks with 3 and 4 elements. We use Legendrian racks to distinguish certain Legendrian knots which are equivalent as smooth knots.
Keywords : Legendrian knot, Legendrian rack, racks with Legendrian structure, contact structure, invariants of Legendrian knots and links