Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies

Abstract

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 $-k$.

Information about $\delta$-graded homology has been changed along with statement of Theorem 1 and Table 1. Significant changes to Section 3

References in corpus (6)

• Floer homology and knot complements
• A combinatorial spanning tree model for knot Floer homology
• Turaev torsion, definite 4-manifolds, and quasi-alternating knots
• Computations of Heegaard-Floer knot homology
• On the skein exact squence for knot Floer homology
• The Khovanov homology of (p,-p,q) pretzel knots

Cited by in corpus (3)

• Mapping cone formula in Heegaard Floer homology and Dehn surgery on knots in $S^3$
• Three-manifold mutations detected by Heegaard Floer homology
• Only finitely many alternating knots can yield a given manifold by surgery