Legendrian Rack Invariants of Legendrian Knots

Jose Ceniceros; Mohamed Elhamdadi; Sam Nelson

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arXiv · 1905.06432

Legendrian Rack Invariants of Legendrian Knots

Jose Ceniceros·Mohamed Elhamdadi·Sam Nelson

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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.

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Jose Ceniceros, Mohamed Elhamdadi, Sam Nelson. 2019-05-15. Legendrian Rack Invariants of Legendrian Knots. https://arxiv.org/abs/1905.06432

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