East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

POLYNOMIAL INVARIANTS OF LONG VIRTUAL KNOTS

  • Im, Young Ho (Department of Mathematics, Pusan National University) ;
  • Kim, Sera (Department of Mathematics, Pusan National University)
  • Received : 2018.07.18
  • Accepted : 2018.11.27
  • Published : 2019.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce a family of polynomial invariants by using intersection index defined from a Gauss diagram of a long virtual knot, and we give some properties for long virtual knots. We extend these polynomials so that we give two-variable polynomial invariants and some example.

Keywords

References

  1. Z. Cheng, A transcendental function invariant of virtual knots, arXiv:1511.08459v1math.GT (2015). https://doi.org/10.2969/jmsj/06941583
  2. A. Henrich, A sequence of degree one Vassiliev Invariants for virtual knots, J. Knot Theory Ramifications 19 (2010), 461-487. https://doi.org/10.1142/S0218216510007917
  3. Y. H. Im and S. Kim, A sequence of polynomial invariants for Gauss diagrams, to appear in J. Knot theory Ramifications.
  4. Y. H. Im and K. Lee, A polynomial invariant of long virtual knots, European J. Combin. 30 (2009) no. 5, 1289-1296. https://doi.org/10.1016/j.ejc.2008.11.011
  5. Y. H. Im, K. Lee and S. Y. Lee, Index polynomial invariant of virtual links, J. Knot Theory Ramifications 19 (2010), no.5, 709-725. https://doi.org/10.1142/S0218216510008042
  6. M. J. Jeong, A zero polynoimal of virtual knots, J. Knot Theory Ramifications 25 (2016), no.1, 1550078. https://doi.org/10.1142/S0218216515500789
  7. L. H. Kauffman, Virtual knot theory, European J. Combin. 20 (1999), 663-690. https://doi.org/10.1006/eujc.1999.0314
  8. V. Manturov, Long virtual knots and their invariants, J. Knot Theory Ramifications 13 (2004) 1029-1039. https://doi.org/10.1142/S0218216504003639
  9. V. Turaev, Lectures on topology of words, Japan J. Math. 2 (2007), 1-39. https://doi.org/10.1007/s11537-007-0634-2
  10. M. Polyak, Minimal generating sets of Reidemeister moves, Quantum Topology 1 (2010), 399-411. https://doi.org/10.4171/QT/10