Geodesic
Distance one lens space fillings and band surgery on the trefoil knot
Lidman, Tye1 ; Moore, Allison2 ; Vazquez, Mariel3
1 Department of Mathematics, North Carolina State University, Raleigh, NC, United States
2 Department of Mathematics, University of California Davis, Davis, CA, United States, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States
3 Department of Mathematics, and Department of Microbiology and Molecular Genetics, University of California Davis, Davis, CA, United States
Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2439-2484

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We prove that if the lens space L(n,1) is obtained by a surgery along a knot in the lens space L(3,1) that is distance one from the meridional slope, then n is in {−6,±1,±2,3,4,7}. This result yields a classification of the coherent and noncoherent band surgeries from the trefoil to T(2,n) torus knots and links. The main result is proved by studying the behavior of the Heegaard Floer d–invariants under integral surgery along knots in L(3,1). 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.

DOI : 10.2140/agt.2019.19.2439
Classification : 57M25, 57M27, 57R58, 92E10
Keywords: lens spaces, Dehn surgery, Heegaard Floer homology, band surgery, torus knots, $d$–invariants, reconnection, DNA topology

Lidman, Tye 1 ; Moore, Allison 2 ; Vazquez, Mariel 3

1 Department of Mathematics, North Carolina State University, Raleigh, NC, United States
2 Department of Mathematics, University of California Davis, Davis, CA, United States, Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA, United States
3 Department of Mathematics, and Department of Microbiology and Molecular Genetics, University of California Davis, Davis, CA, United States 
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Lidman, Tye; Moore, Allison; Vazquez, Mariel. Distance one lens space fillings and band surgery on the trefoil knot. Algebraic and Geometric Topology, Tome 19 (2019) no. 5, pp. 2439-2484. doi: 10.2140/agt.2019.19.2439

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