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We generalize some of the congruences in \cite{P} to periodic knotted trivalent graphs. As an application, a criterion derived from one of these congruences is used to obstruct periodicity of links of few crossings for the odd primes $p=3,5,7,$ and 11. Moreover, we derive a new criterion of periodic links. In particular, we give a sufficient condition for the period to divide the crossing number. This gives some progress toward solving the well-known conjecture that the period divides the crossing number in the case of alternating links.
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참고문헌 (25)
참고문헌 신청
C. Adams / 1991 / Hyperbolic invariants of knots and links / Trans. Amer. Math. Soc. 326(1):1~56
D. Bar-Natan / 0000 / The Mathematica package KnotTheory
G. Burde / 2003 / Knots, second edition, De Gruyter Studies in Mathematics, 5
Carmen Caprau / 2015 / The Kauffman Polynomial and Trivalent Graphs / Kyungpook Mathematical Journal 55(4):779~806
N. Chbili / 2008 / Strong periodicity of links and the coefficients of the Conway polynomial / Proc. Amer. Math. Soc. 136(6):2217~2224
D. Bar-Natan / 0000 / The Mathematica package KnotTheory
G. Burde / 2003 / Knots, second edition, De Gruyter Studies in Mathematics, 5
Carmen Caprau / 2015 / The Kauffman Polynomial and Trivalent Graphs / Kyungpook Mathematical Journal 55(4):779~806
N. Chbili / 2008 / Strong periodicity of links and the coefficients of the Conway polynomial / Proc. Amer. Math. Soc. 136(6):2217~2224
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