• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.623-639
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• 2021

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.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.789-804
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• 2019

In this paper, we prove that a link which has an almost positive diagram with a certain condition is Lagrangian fillable.