Algebraic & Geometric Topology Volume 7, issue 3 (2007)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

A skein relation for the HOMFLYPT polynomials of two-cable links

Taizo Kanenobu

Algebraic & Geometric Topology 7 (2007) 1211–1232

DOI: 10.2140/agt.2007.7.1211

Bibliography

1	J H Conway, An enumeration of knots and links, and some of their algebraic properties, from: "Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967)", Pergamon (1970) 329 MR0258014
2	D De Wit, Automatic evaluation of the Links–Gould invariant for all prime knots of up to 10 crossings, J. Knot Theory Ramifications 9 (2000) 311 MR1753798
3	D De Wit, J Links, Where the Links–Gould invariant first fails to distinguish nonmutant prime knots arXiv:math.GT/0501224v2
4	D De Wit, J R Links, L H Kauffman, On the Links–Gould invariant of links, J. Knot Theory Ramifications 8 (1999) 165 MR1687549
5	P Freyd, D Yetter, J Hoste, W B R Lickorish, K Millett, A Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. $($N.S.$)$ 12 (1985) 239 MR776477
6	J Hoste, M Thistlethwaite, J Weeks, The first 1,701,936 knots, Math. Intelligencer 20 (1998) 33 MR1646740
7	A Ishii, Algebraic links and skein relations of the Links–Gould invariant, Proc. Amer. Math. Soc. 132 (2004) 3741 MR2084099
8	A Ishii, T Kanenobu, Different links with the same Links–Gould invariant, Osaka J. Math. 42 (2005) 273 MR2147736
9	V F R Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. $(2)$ 126 (1987) 335 MR908150
10	T Kanenobu, Infinitely many knots with the same polynomial invariant, Proc. Amer. Math. Soc. 97 (1986) 158 MR831406
11	T Kanenobu, Examples on polynomial invariants of knots and links, Math. Ann. 275 (1986) 555 MR859330
12	T Kanenobu, Examples on polynomial invariants of knots and links. II, Osaka J. Math. 26 (1989) 465 MR1021426
13	T Kanenobu, Kauffman polynomials for $2$–bridge knots and links, Yokohama Math. J. 38 (1991) 145 MR1105072
14	T Kanenobu, Genus and Kauffman polynomial of a $2$–bridge knot, Osaka J. Math. 29 (1992) 635 MR1181126
15	T Kanenobu, T Sumi, Polynomial invariants of $2$–bridge links through $20$ crossings, from: "Aspects of low-dimensional manifolds", Adv. Stud. Pure Math. 20, Kinokuniya (1992) 125 MR1208310
16	T Kanenobu, T Sumi, Polynomial invariants of $2$–bridge knots through $22$ crossings, Math. Comp. 60 (1993) 771 MR1176711
17	L H Kauffman, On Knots, Ann. of Math. Studies, Princeton University Press, Princeton (1987)
18	L H Kauffman, An invariant of regular isotopy, Trans. Amer. Math. Soc. 318 (1990) 417 MR958895
19	W B R Lickorish, A S Lipson, Polynomials of $2$–cable-like links, Proc. Amer. Math. Soc. 100 (1987) 355 MR884479
20	W B R Lickorish, K C Millett, A polynomial invariant of oriented links, Topology 26 (1987) 107 MR880512
21	J R Links, M D Gould, Two variable link polynomials from quantum supergroups, Lett. Math. Phys. 26 (1992) 187 MR1199742
22	H R Morton, H B Short, The $2$–variable polynomial of cable knots, Math. Proc. Cambridge Philos. Soc. 101 (1987) 267 MR870598
23	J H Przytycki, Equivalence of cables of mutants of knots, Canad. J. Math. 41 (1989) 250 MR1001611
24	J H Przytycki, P Traczyk, Invariants of links of Conway type, Kobe J. Math. 4 (1988) 115 MR945888
25	D Rolfsen, Knots and links, Publish or Perish (1976) MR0515288
26	A Stoimenow, On cabled knots and Vassiliev invariants (not) contained in knot polynomials, Canad. J. Math. 59 (2007) 418 MR2310624
27	J M Van Buskirk, A class of negative-amphicheiral knots and their Alexander polynomials, Rocky Mountain J. Math. 13 (1983) 413 MR715764
28	S Yamada, On the two variable Jones polynomial of satellite links, from: "Topology and computer science (Atami, 1986)", Kinokuniya (1987) 295 MR1112599