|
Algebraic links and skein relations of the Links-Gould invariant
Author(s):
Atsushi
Ishii
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3741-3749.
MSC (2000):
Primary 57M27
Posted:
July 26, 2004
MathSciNet review:
2084099
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We give certain skein relations of the Links-Gould invariant. We also show that the relations lead us to recursive calculation of the invariant for algebraic links. As an application we give a formula for the Links-Gould invariant of 2-bridge links.
References:
-
- 1.
- J.H. Conway, An enumeration of knots and links, and some of their algebraic properties, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967), Pergamon Press, Oxford, 1970, pp. 329-350. MR 41:2661
- 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), no.3, 311-339. MR 2001d:57015
- 3.
- D. De Wit, An infinite suite of Links-Gould invariants, J. Knot Theory Ramifications. 10 (2001), no.1, 37-62. MR 2002e:57015
- 4.
- D. De Wit, L.H. Kauffman and J.R. Links, On the Links-Gould invariant of links, J. Knot Theory Ramifications. 8 (1999), no.2, 165-199. MR 2000j:57020
- 5.
- A. Ishii, The Links-Gould invariant of closed 3-braids, J. Knot Theory Ramifications. 13 (2004), no.1, 41-56.
- 6.
- J.R. Links and M.D. Gould, Two variable link polynomials from quantum supergroups, Lett. Math. Phys. 26 (1992), no.3, 187-198. MR 93k:57018
- 7.
- J.H. Przytycki, Skein modules of 3-manifolds, Bull. Ac. Pol. Math. 39 (1991), 91-100. MR 94g:57011
- 8.
- V.G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988), no.3, 527-553. MR 89e:57003
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
57M27
Retrieve articles in all Journals with
MSC (2000):
57M27
Additional Information:
Atsushi
Ishii
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-16, Toyonaka, Osaka 560-0043, Japan
Email:
aishii@cr.math.sci.osaka-u.ac.jp
DOI:
10.1090/S0002-9939-04-07481-7
PII:
S 0002-9939(04)07481-7
Keywords:
Links-Gould invariant,
skein relation
Received by editor(s):
June 9, 2003
Received by editor(s) in revised form:
July 29, 2003
Posted:
July 26, 2004
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
2004,
American Mathematical Society
|
