Jose Ceniceros, Mohamed Elhamdadi, Sam Nelson 198 College Hill Rd.; 4202 E Fowler Ave.; 850 Columbia Ave.
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
MSC numbers : 57M27, 57M25
Supported by : Partially supported by Simons Foundation collaboration grant 316709.