#### Volume 15, issue 1 (2015)

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

### Allison H Moore and Laura Starkston

Algebraic & Geometric Topology 15 (2015) 43–63
##### 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 $-k$.

##### Keywords
mutation, genus-two mutation, Heegaard Floer, Khovanov
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57R58
##### Publication
Revised: 19 November 2012
Accepted: 12 July 2014
Published: 23 March 2015
##### Authors
 Allison H Moore Department of Mathematics The University of Texas 2515 Speedway Stop C1200 Austin, TX 78712 USA http://www.ma.utexas.edu/~moorea8 Laura Starkston Department of Mathematics The University of Texas 2515 Speedway Stop C1200 Austin, TX 78712 USA http://www.ma.utexas.edu/~lstarkston