The Links-Gould Invariant as a Classical Generalization of the Alexander Polynomial?

被引：1

作者：

Kohli, Ben-Michael ^{[1
]}

机构：

[1] Univ Bourgogne Franche Comte, Inst Math Bourgogne, Dijon, France

来源：

EXPERIMENTAL MATHEMATICS | 2018年 / 27卷 / 03期

关键词：

Alexander-Conway polynomial; fibredness; genus; knot; link; Links-Gould invariant; SUBGROUP; GENUS;

D O I：

10.1080/10586458.2016.1255860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we conjecture that the Links-Gould invariant of links, which we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular, it seems to give a lower bound for the genus of links and to provide a criterion for fibredness of knots. We give some evidence for these two assumptions.

引用

页码：251 / 264

页数：14

共 50 条

[1] On the Links-Gould invariant and the square of the Alexander polynomial
Kohli, Ben-Michael
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2016, 25 (02)
[2] The Links-Gould polynomial as a generalization of the Alexander-Conway polynomial
Ishii, Atsushi
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2006, 225 (02) : 273 - 285
[3] On the Links-Gould invariant of links
De Wit, D
Links, JR
Kauffman, LH
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 1999, 8 (02) : 165 - 199
[4] OTHER QUANTUM RELATIVES OF THE ALEXANDER POLYNOMIAL THROUGH THE LINKS-GOULD INVARIANTS
Kohli, Ben-Michael
Patureau-Mirand, Bertrand
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (12) : 5419 - 5433
[5] Different links with the same links-gould invariant
Ishii, A
Kanenobu, T
[J]. OSAKA JOURNAL OF MATHEMATICS, 2005, 42 (02) : 273 - 290
[6] Algebraic links and Skein relations of the Links-Gould invariant
Ishii, A
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (12) : 3741 - 3749
[7] A cubic defining algebra for the Links-Gould polynomial
Marin, Ivan
Wagner, Emmanuel
[J]. ADVANCES IN MATHEMATICS, 2013, 248 : 1332 - 1365
[8] The Links-Gould invariant of closed 3-braids
Ishii, A
[J]. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2004, 13 (01) : 41 - 56
[9] The Leading Finite Type Coefficients of the Links-Gould Polynomial of a Link
Ishii, Atsushi
[J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2010, 50 (01): : 49 - 58
[10] A combinatorial description of the centralizer algebras connected to the Links-Gould invariant
Anghel, Cristina Ana-Maria
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2021, 21 (03): : 1553 - +

← 1 2 3 4 5 →