2005/01/20 by Sangyop Lee, Lee, Sangyop, Masakazu Teragaito +1
Mathematics · #57M50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT #msc:57M50
paper · pdf · doi:10.48550/arxiv.math/0501316
22 pages, 10 figures: change of the title, and minor corrections
openalex publication_date 2005/01/20 · arxiv created 2005/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a hyperbolic 3-manifold M with a torus boundary component,all but finitely many Dehn fillings yield hyperbolic 3-manifolds. In this paper, we will focus on the situation where M has two exceptional Dehn fillings: an annular filling and a toroidal filling. For such situation, Gordon gave an upper bound 5 for the distance between such slopes. Furthermore, the distance 4 is realized only by two specific manifolds, and 5 is realized by a single manifold. These manifolds all have a union of two tori as their boundaries. Also, there is a manifold with three tori as its boundary which realizes the distance 3. We show that if the distance is three then the boundary of the manifold consists of at most three tori.