Classical homological invariants are not determined by knot Floer homology and Khovanov homology

被引：0

作者：

Cha, Jae Choon ^{[1
,2
]}

Tanaka, Toshifumi ^{[3
]}

机构：

[1] POSTECH, Dept Math, Pohang 790784, South Korea

[2] Korea Inst Adv Study, Sch Math, Seoul 130722, South Korea

[3] Gifu Univ, Fac Educ, Dept Math, Yanagido 1-1, Gifu 5011193, Japan

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2016年 / 25卷 / 07期

基金：

新加坡国家研究基金会;

关键词：

Knots; knot Floer homology; Khovanov homology; Alexander module; symmetric union; POLYNOMIAL INVARIANT; BRAID INVARIANTS;

D O I：

10.1142/S0218216516500395

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We illustrate that there are knots for which Heegaard knot Floer homology and Khovanov homology are identical but the Alexander module and torsion invariants differ. The examples are certain symmetric unions. We also give examples of similar flavor, concerning the Kauffman and Q-polynomials in place of the classical homological invariants. This shows there are nonmutant knots with the same knot Floer and Khovanov homology.

引用

页数：14

共 50 条

[21] Homological actions on sutured Floer homology
Ni, Yi
MATHEMATICAL RESEARCH LETTERS, 2014, 21 (05) : 1177 - 1197
[22] Khovanov homology and the symmetry group of a knot
Watson, Liam
ADVANCES IN MATHEMATICS, 2017, 313 : 915 - 946
[23] Extremal Khovanov homology and the girth of a knot
Sazdanovic, Radmila
Scofield, Daniel
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2022, 31 (13)
[24] On transverse invariants from Khovanov homology
Lipshitz, Robert
Ng, Lenhard
Sarkar, Sucharit
QUANTUM TOPOLOGY, 2015, 6 (03) : 475 - 513
[25] A surgery formula for knot Floer homology
Hedden, Matthew
Levine, Adam Simon
QUANTUM TOPOLOGY, 2024, 15 (02) : 229 - 336
[26] On the geography and botany of knot Floer homology
Matthew Hedden
Liam Watson
Selecta Mathematica, 2018, 24 : 997 - 1037
[27] On the geography and botany of knot Floer homology
Hedden, Matthew
Watson, Liam
SELECTA MATHEMATICA-NEW SERIES, 2018, 24 (02): : 997 - 1037
[28] On Knot Floer Homology and Cabling: 2
Hedden, Matthew
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2009, 2009 (12) : 2248 - 2274
[29] Twisting, mutation and knot Floer homology
Lambert-Cole, Peter
QUANTUM TOPOLOGY, 2018, 9 (04) : 749 - 774
[30] Knot Floer homology and Seifert surfaces
Juhasz, Andras
ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2008, 8 (01): : 603 - 608

← 1 2 3 4 5 →