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Hyperbolic 3-manifolds of low cusp volume

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arxiv 2109.14570 v1 pith:5QE52GCV submitted 2021-09-29 math.GT

David Gabai , Robert Haraway , Robert Meyerhoff , Nathaniel Thurston , Andrew Yarmola This is my paper · ORCID
classification math.GT
keywords hyperbolicmanifoldsvolumecomplementcuspcuspedfigure-8knot
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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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  1. Hyperbolic manifolds without positive spun triangulations

    math.GT 2026-07 accept novelty 7.5 of 10

    Vol3 with its systole or second-shortest geodesic admits no positive spun ideal triangulation, by Choi's criterion applied to explicit shape varieties of census fillings.

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