2003/12/10 by Masakazu Teragaito, Teragaito, Masakazu
Mathematics · #57M25 #57M50 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25 #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0312201
25 pages, 19 figures: Minor corrections were done for publication
openalex publication_date 2003/12/10 · arxiv created 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic 3-manifolds. As a typical case of such an exceptional surgery, a toroidal surgery is one that yields a closed 3-manifold containing an incompressible torus. The slope corresponding to a toroidal surgery, called a toroidal slope, is known to be integral or half-integral. We show that the distance between two integral toroidal slopes for a hyperbolic knot, except the figure-eight knot, is at most four. Hence any hyperbolic knot admits at most 5 toroidal surgeries.