Legendrian rack invariants of Legendrian knots
Commun. Korean Math. Soc. 2021 Vol. 36, No. 3, 623-639
Published online March 18, 2021
Printed July 31, 2021
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.
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