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http://dx.doi.org/10.4134/CKMS.c200251

LEGENDRIAN RACK INVARIANTS OF LEGENDRIAN KNOTS  

Ceniceros, Jose (Department of Mathematics Hamilton College)
Elhamdadi, Mohamed (Department of Mathematics University of South Florida)
Nelson, Sam (Department of Mathematics Claremont McKenna College)
Publication Information
Communications of the Korean Mathematical Society / v.36, no.3, 2021 , pp. 623-639 More about this Journal
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;
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