Hyperbolic 3-manifolds of low cusp volume

2021/09/29 by David Gabai, Gabai, David, Robert C. Haraway +7
Computer Science · Mathematics · #51M10 #51M25 #57M50 #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2109.14570

openalex publication_date 2021/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the complete hyperbolic 3-manifolds admitting a maximal cusp of volume at most 2.62. We use this to show that the figure-8 knot complement is the unique 1-cusped hyperbolic 3-manifold with nine or more non-hyperbolic fillings; to show that the figure-8 knot complement and its sister are the unique hyperbolic 3-manifolds with minimal volume maximal cusps; and to extend results on determining low volume closed and cusped hyperbolic 3-manifolds.

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