Dichromatic link invariants

作者: Jim Hoste , Mark E. Kidwell

DOI: 10.1090/S0002-9947-1990-0961623-2

关键词: MathematicsBracket polynomialKnot theoryAlexander polynomialKnot polynomialPure mathematicsKauffman polynomialAlgebraHOMFLY polynomialJones polynomialInvariant (mathematics)

摘要: We investigate the skein theory of oriented dichromatic links in S3. define a new chromatic invariant for special class links. This generalizes both two-variable Alexander polynomial and twisted polynomial. Alternatively, one may view this 1 2 as an monochromatic S x D , such it is exact analog discuss basic properties applications to link interchangeability. For full we show that there does not exist which mutual extension

参考文章(15)
Jozef H. Przytycki, Pawel Traczyk, Invariants of links of Conway type Kobe journal of mathematics. ,vol. 4, pp. 115- 139 ,(1988)
J.H. CONWAY, An enumeration of knots and links, and some of their algebraic properties Computational Problems in Abstract Algebra#R##N#Proceedings of a Conference Held at Oxford Under the Auspices of the Science Research Council Atlas Computer Laboratory, 29th August to 2nd September 1967. pp. 329- 358 ,(1970) , 10.1016/B978-0-08-012975-4.50034-5
Dale Rolfsen, Knots and Links ,(2003)
Jim Hoste, J{ózef H. Przytycki, An invariant of dichromatic links Proceedings of the American Mathematical Society. ,vol. 105, pp. 1003- 1007 ,(1989) , 10.1090/S0002-9939-1989-0989100-0
Robert D. Brandt, W. B. R. Lickorish, Kenneth C. Millett, A polynomial invariant for unoriented knots and links Inventiones Mathematicae. ,vol. 84, pp. 563- 573 ,(1986) , 10.1007/BF01388747
V G Turaev, Reidemeister torsion in knot theory Russian Mathematical Surveys. ,vol. 41, pp. 119- 182 ,(1986) , 10.1070/RM1986V041N01ABEH003204
Richard Hartley, The conway potential function for links Commentarii Mathematici Helvetici. ,vol. 58, pp. 365- 378 ,(1983) , 10.1007/BF02564642
Louis H. Kauffman, New invariants in the theory of knots American Mathematical Monthly. ,vol. 95, pp. 195- 242 ,(1988) , 10.2307/2323625
Jim Hoste, A polynomial invariant of knots and links Pacific Journal of Mathematics. ,vol. 124, pp. 295- 320 ,(1986) , 10.2140/PJM.1986.124.295
W. B. R. Lickorish, K. C. Millett, The New Polynomial Invariants of Knots and Links Mathematics Magazine. ,vol. 61, pp. 3- 23 ,(1988) , 10.1080/0025570X.1988.11977338