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

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