대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제36권3호
  • /
  • Pages.623-639
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  • 2021
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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LEGENDRIAN RACK INVARIANTS OF LEGENDRIAN KNOTS

  • 투고 : 2020.07.18
  • 심사 : 2021.01.08
  • 발행 : 2021.07.31
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초록

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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과제정보

Partially supported by Simons Foundation collaboration grant 316709.

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