Communications of the
Korean Mathematical Society

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024



Commun. Korean Math. Soc. 2021; 36(3): 623-639

Online first article March 18, 2021      Printed July 31, 2021

Copyright © The Korean Mathematical Society.

Legendrian rack invariants of Legendrian knots

Jose Ceniceros, Mohamed Elhamdadi, Sam Nelson

198 College Hill Rd.; 4202 E Fowler Ave.; 850 Columbia Ave.


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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