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 –gradings and .
Citation
Allison H Moore. Laura Starkston. "Genus-two mutant knots with the same dimension in knot Floer and Khovanov homologies." Algebr. Geom. Topol. 15 (1) 43 - 63, 2015. https://doi.org/10.2140/agt.2015.15.43
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