Genus-two mutant knots with the same dimension in knot Floer and Khovanov homologies. (English) Zbl 1314.57009
Summary: We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus-two mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus-two mutant by both knot Floer homology and Khovanov homology as bigraded groups. Additionally, for both knot Heegaard Floer homology and Khovanov homology, the genus-two mutation interchanges the groups in \(\delta\)-gradings \(k\) and \(-k\).
MSC:
| 57M25 | Knots and links in the \(3\)-sphere (MSC2010) |
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57R58 | Floer homology |
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