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

Allison Moore; Laura Starkston

doi:10.2140/agt.2015.15.43

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arXiv · 1204.2524

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

Allison Moore·Laura Starkston

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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 $δ$-gradings $k$ and $-k$.

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BibTeX RIS

Allison Moore, Laura Starkston. 2012-11-20. Genus two mutant knots with the same dimension in knot Floer and Khovanov homologies. https://doi.org/10.2140/agt.2015.15.43

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