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Genus-two mutant knots
with the same dimension in knot Floer and Khovanov
homologies
Allison H Moore and Laura Starkston |
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Algebraic & Geometric Topology 15 (2015) 43–63
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Abstract |
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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 . |
Keywords
mutation, genus-two mutation, Heegaard Floer, Khovanov
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57R58
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References |
Publication
Received: 4 June 2012
Revised: 19 November 2012
Accepted: 12 July 2014
Published: 23 March 2015
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Authors |
| Allison H Moore | |
| Department of Mathematics The University of Texas 2515 Speedway Stop C1200 Austin, TX 78712 USA |
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| http://www.ma.utexas.edu/~moorea8 | |
| Laura Starkston | |
| Department of Mathematics The University of Texas 2515 Speedway Stop C1200 Austin, TX 78712 USA |
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| http://www.ma.utexas.edu/~lstarkston | |
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