Hyperbolic 3-manifolds of low cusp volume

David Gabai; Robert Haraway; Robert Meyerhoff; Nathaniel Thurston; Andrew Yarmola

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arXiv · 2109.14570

Hyperbolic 3-manifolds of low cusp volume

David Gabai·Robert Haraway·Robert Meyerhoff·Nathaniel Thurston·Andrew Yarmola

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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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David Gabai, Robert Haraway, Robert Meyerhoff, Nathaniel Thurston, Andrew Yarmola. 2021-09-29. Hyperbolic 3-manifolds of low cusp volume. https://arxiv.org/abs/2109.14570

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