Geodesic
Finite Dehn surgeries on knots in S3
Ni, Yi1 ; Zhang, Xingru2
1 Department of Mathematics, California Institute of Technology, Pasadena, CA, United States
2 Department of Mathematics, University at Buffalo, Buffalo, NY, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 441-492

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

We show that on a hyperbolic knot K in S3, the distance between any two finite surgery slopes is at most 2, and consequently, there are at most three nontrivial finite surgeries. Moreover, in the case where K admits three nontrivial finite surgeries, K  must be the pretzel knot P(−2,3,7). In the case where K admits two noncyclic finite surgeries or two finite surgeries at distance 2, the two surgery slopes must be one of ten or seventeen specific pairs, respectively. For D–type finite surgeries, we improve a finiteness theorem due to Doig by giving an explicit bound on the possible resulting prism manifolds, and also prove that 4m and 4m + 4 are characterizing slopes for the torus knot T(2m + 1,2) for each m ≥ 1.

DOI : 10.2140/agt.2018.18.441
Classification : 57M25
Keywords: finite Dehn surgery, Culler-Shalen norm, Heegaard Floer homology

Ni, Yi 1 ; Zhang, Xingru 2

1 Department of Mathematics, California Institute of Technology, Pasadena, CA, United States
2 Department of Mathematics, University at Buffalo, Buffalo, NY, United States 
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Ni, Yi; Zhang, Xingru. Finite Dehn surgeries on knots in S3. Algebraic and Geometric Topology, Tome 18 (2018) no. 1, pp. 441-492. doi: 10.2140/agt.2018.18.441

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