THE JONES AND ALEXANDER POLYNOMIALS FOR SINGULAR LINKS

被引：10

作者：

Fiedler, Thomas ^{[1
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse 09, France

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2010年 / 19卷 / 07期

关键词：

Classical and singular links; knot polynomials; state models;

D O I：

10.1142/S0218216510008236

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the Kauffman state models of the Jones and Alexander polynomials of classical links to state models of their two-variable extensions in the case of singular links. Moreover, we extend both of them to polynomials with d + 1 variables for long singular knots with exactly d double points. These extensions can detect non-invertibility of long singular knots.

引用

页码：859 / 866

页数：8

共 50 条

[1] Alexander and Jones polynomials of weaving 3-braid links and Whitney rank polynomials of Lucas lattice
Alsukaiti, Mark E.
Chbili, Nafaa
[J]. HELIYON, 2024, 10 (07)
[2] ALEXANDER POLYNOMIALS OF RIBBON LINKS
Hillman, Jonathan A.
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2011, 20 (02) : 327 - 331
[3] On Alexander Polynomials of Pretzel Links
Bae, Yongju
Lee, In Sook
[J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2020, 60 (02): : 239 - 253
[4] JONES POLYNOMIALS OF ALTERNATING LINKS
MURASUGI, K
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 295 (01) : 147 - 174
[5] JONES POLYNOMIALS OF PERIODIC LINKS
MURASUGI, K
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1988, 131 (02) : 319 - 329
[6] On links with cyclotomic Jones polynomials
Champanerkar, Abhijit
Kofman, Ilya
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2006, 6 : 1655 - 1668
[7] Twisted Alexander Polynomials of Hyperbolic Links
Morifuji, Takayuki
Tran, Anh T.
[J]. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2017, 53 (03) : 395 - 418
[8] The Alexander polynomials of immersed concordant links
Akio Kawauchi
[J]. Boletín de la Sociedad Matemática Mexicana, 2014, 20 (2) : 559 - 578
[9] Realizing Alexander polynomials by hyperbolic links
Stoimenow, A.
[J]. EXPOSITIONES MATHEMATICAE, 2010, 28 (02) : 133 - 178
[10] Twisted Alexander polynomials of torus links
Kitano, Teruaki
Morifuji, Takayuki
Tran, Anh T.
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2020, 29 (04)

← 1 2 3 4 5 →