대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권2호
  • /
  • Pages.303-318
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  • 2022
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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VARIATIONS IN WRITHES OF VIRTUAL KNOTS UNDER A LOCAL MOVE

  • Gill, Amrendra (Department of Mathematics Indian Institute of Technology Ropar) ;
  • Madeti, Prabhakar (Department of Mathematics Indian Institute of Technology Ropar)
  • 투고 : 2020.11.03
  • 심사 : 2021.11.05
  • 발행 : 2022.03.31
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초록

n-writhes denoted by Jn(K) are virtual knot invariants for n ≠ 0 and are closely associated with coefficients of some polynomial invariants of virtual knots. In this work, we investigate the variations of Jn(K) under arc shift move and conclude that n-writhes Jn(K) vary randomly in the sense that it may change by any random integer value under one arc shift move. Also, for each n ≠ 0 we provide an infinite family of virtual knots which can be distinguished by n-writhes Jn(K), whereas odd writhe J(K) fails to do so.

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참고문헌

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