2004/10/18 by Suhyoung Choi, Choi, Suhyoung · 1 citation
Computer Science · Mathematics · #57M50 #Computational Geometry and Mesh Generation #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/0410381
50 pages, 3 figures
arxiv created 2004/10/18 · openalex publication_date 2004/10/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We supply a proof of the fact that a hyperbolic 3-manifold M with finitely generated fundamental group and with no parabolics is topologically tame. This proves the Marden's conjecture. Our approach is to form an exhaustion Mi of M and modify the boundary to make them 2-convex. We use the induced path-metric, which makes the submanifold Mi δ-hyperbolic and with Margulis constants independent of i. By taking the convex hull in the cover of Mi corresponding the core, we show that there exists an exiting sequence of surfaces Σi. We drill out the covers of Mi by a core C again to make it δ-hyperbolic. Then the boundary of the convex hull of Σi is shown to meet the core. By the compactness argument of Souto, we show that infinitely many of Σi are homotopic in M - Co.