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Distance one lens space
fillings and band surgery on the trefoil knot
Tye Lidman, Allison H Moore and Mariel Vazquez |
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Algebraic & Geometric Topology 19 (2019) 2439–2484
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Abstract |
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We prove that if the lens space is obtained by a surgery along a knot in the lens space that is distance one from the meridional slope, then is in . This result yields a classification of the coherent and noncoherent band surgeries from the trefoil to torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer –invariants under integral surgery along knots in . The classification of band surgeries between the trefoil and torus knots and links is motivated by local reconnection processes in nature, which are modeled as band surgeries. Of particular interest is the study of recombination on circular DNA molecules. |
Keywords
lens spaces, Dehn surgery, Heegaard Floer homology, band
surgery, torus knots, $d$–invariants, reconnection, DNA
topology
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27, 57R58
Secondary: 92E10
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References |
Publication
Received: 19 December 2017
Revised: 12 August 2018
Accepted: 16 October 2018
Published: 20 October 2019
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Authors |
| Tye Lidman | |
| Department of Mathematics North Carolina State University Raleigh, NC United States |
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| Allison H Moore | |
| Department of Mathematics University of California Davis Davis, CA United States |
Department of Mathematics and
Applied Mathematics Virginia Commonwealth University Richmond, VA United States |
| Mariel Vazquez | |
| Department of Mathematics, and
Department of Microbiology and Molecular Genetics University of California Davis Davis, CA United States |
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