2005/12/01 by Cameron McA. Gordon, Gordon, Cameron McA., Ying-Qing Wu +1
Mathematics · #57N10 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/0512038
openalex publication_date 2005/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We determine all hyperbolic 3-manifolds M admitting two toroidal Dehn fillings at distance 4 or 5. We show that if M is a hyperbolic 3-manifold with a torus boundary component T0, and r,s are two slopes on T0 with Δ(r,s) = 4 or 5 such that M(r) and M(s) both contain an essential torus, then M is either one of 14 specific manifolds Mi, or obtained from M1, M2, M3 or M14 by attaching a solid torus to ∂ Mi - T0. All the manifolds Mi are hyperbolic, and we show that only the first three can be embedded into S3. As a consequence, this leads to a complete classification of all hyperbolic knots in S3 admitting two toroidal surgeries with distance at least 4.