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

Jae Choon Cha

Department of Mathematics, POSTECH, Pohang 790-784, Republic of Korea

School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Republic of Korea

E-mail Address: jccha@postech.ac.kr

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and

Toshifumi Tanaka

Faculty of Education, Department of Mathematics, Gifu University, Yanagido 1-1, Gifu 501-1193, Japan

E-mail Address: tanakat@gifu-u.ac.jp

Corresponding author.

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https://doi.org/10.1142/S0218216516500395Cited by:0 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M25, 57M27

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