A polynomial invariant of polar links
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Knots were generalized to virtual knots by L. H. Kauffman. We introduce polar knots and polar links, another generalization of knots, which are motivated by links in the complement of the z-axis in R3. There are no knots and no virtual knots with crossing number 1 but we show that there are two polar knots with crossing number 1. We introduce a bracket polynomial of polar links and get an invariant of oriented polar links.
Abstract
Knots were generalized to virtual knots by L. H. Kauffman. We introduce polar knots and polar links, another generalization of knots, which are motivated by links in the complement of the z-axis in R3. There are no knots and no virtual knots with crossing number 1 but we show that there are two polar knots with crossing number 1. We introduce a bracket polynomial of polar links and get an invariant of oriented polar links.
참고문헌 (10)
- M. Goussarov, "Finite type invariants of classical and virtual knots", Topology, 39, pp.1045~1068 (2000)
- C. F. Ho, "A new polynomial invariant for knots and links–preliminary report", Abstracts Amer. Math. Soc., 6, pp.300~ (1985)
- P. Freyd, "A new polynomial invariant of knots and links", Bull. Amer. Math. Soc., 12, pp.239~246 (1985)
- M.–J. Jeong, "Reidemeister moves and a polynomial of virtual knot diagrams", J. of Knot Theory and Its Ramifications, 24(2), pp.16~ (2015)
- M.–J. Jeong, "A zero polynomial of virtual knots", J. of Knot Theory and Its Ramifications, 25(1), pp.19~ (2015)
- V. F. R. Jones, "A polynomial invariant for knots via von Neumann algebras", Bull. Amer. Math. Soc., 12, pp.103~112 (1985)
- L. H. Kauffman, "State models and the Jones polynomial", Topology, 26, pp.395~407 (1987)
- L. Kauffman, "An invariant of regular isotopy", Trans. Amer. Math. Soc., 318, pp.417~471 (1990)
- L. H. Kauffman, "Virtual knot theory", Europ. J. Combinatorics, 20, pp.663~691 (1999)
- K. Reidemeister, "Elementare Berundang der Knotentheorie", Abh. Math. Sem. Univ. Hamburg, 5, pp.24~32 (1926)