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

Moore, Allison H; Starkston, Laura

doi:10.2140/agt.2015.15.43

Moore, Allison H ¹ ; Starkston, Laura ¹

¹Department of Mathematics, The University of Texas, 2515 Speedway Stop C1200, Austin, TX 78712, USA

Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 43-63

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Résumé

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.

DOI : 10.2140/agt.2015.15.43

Classification : 57M25, 57M27, 57R58
Keywords: mutation, genus-two mutation, Heegaard Floer, Khovanov

Affiliations des auteurs :

Moore, Allison H ¹ ; Starkston, Laura ¹

¹ Department of Mathematics, The University of Texas, 2515 Speedway Stop C1200, Austin, TX 78712, USA

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     author = {Moore, Allison H and Starkston, Laura},
     title = {Genus-two mutant knots with the same dimension in knot {Floer} and {Khovanov} homologies},
     journal = {Algebraic and Geometric Topology},
     pages = {43--63},
     year = {2015},
     volume = {15},
     number = {1},
     doi = {10.2140/agt.2015.15.43},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2015.15.43/}
}

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Moore, Allison H; Starkston, Laura. Genus-two mutant knots with the same dimension in knot Floer and Khovanov homologies. Algebraic and Geometric Topology, Tome 15 (2015) no. 1, pp. 43-63. doi: 10.2140/agt.2015.15.43

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