2012/06/30 by Yi Ni, Xingru Zhang · 30 citations
Mathematics · #Advanced Combinatorial Mathematics #Combinatorics #Floer homology #Geometric and Algebraic Topology #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Mathematics #Symplectic geometry #Torus #math.GT #msc:57M27 #msc:57R58
paper · pdf · doi:10.2140/agt.2014.14.1249
published in Algebraic & Geometric Topology 14(3), 1249-1274 (Mathematical Sciences Publishers) · Version 2: 19 pages. This is a major revision. The title of the first version was "Towards a Dehn surgery characterization of $T_{5,2}$". We extended the result in the first version to general torus knots. We also fixed a gap in the first version, so our result for $T_{5,2}$ is slightly weaker than the originally claimed one
arxiv created 2012/12/02 · openalex publication_date 2014/04/07 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A slope p q is called a characterizing slope for a given knot K 0 in S 3 if whenever the p q -surgery on a knot K in S 3 is homeomorphic to the p q -surgery on K 0 via an orientation preserving homeomorphism, then K D K 0 . In this paper we try to find characterizing slopes for torus knots T r;s . We show that any slope p q which is larger than the number 30.r 2 1/.s 2 1/=67 is a characterizing slope for T r;s . The proof uses Heegaard Floer homology and Agol-Lackenby's 6-theorem. In the case of T 5;2 , we obtain more specific information about its set of characterizing slopes by applying further Heegaard Floer homology techniques.