The maximal number of exceptional Dehn surgeries

2008/08/08 by Marc Lackenby, Lackenby, Marc, Robert Meyerhoff +1 · 2 citations
Mathematics · #57M50 #57N10 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0808.1176

openalex publication_date 2008/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove two conjectures of C. Gordon. We show that the maximal number of exceptional Dehn surgeries on a 1-cusped hyperbolic 3-manifold is 10, and that the maximal intersection number between exceptional slopes is 8. The proof uses a combination of new geometric techniques and a rigorous computer-assisted calculation.

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• A note on the tetrahedral index and the Hahn-Exton q-Bessel function
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