Minimum-volume hyperbolic 3-manifolds

Abstract

We enumerate the small-volume manifolds that can be obtained by Dehn filling on Mom-2 and Mom-3 manifolds as defined by Gabai, Meyerhoff, and the author. In so doing we complete the proof that the Weeks manifold is the minimum-volume compact hyperbolic 3-manifold, as well as enumerating the 10 smallest one-cusped hyperbolic 3-manifolds.

14 pages; updated and added references, provided a stronger argument regarding Vol3 in section 3, incorporated many helpful comments from Craig Hodgson regarding wording and terminology; corrected references

References in corpus (1)

• Proving a manifold to be hyperbolic once it has been approximated to be so

Cited by in corpus (14)

• Solving 3d Gravity with Virasoro TQFT
• Symmetric links and Conway sums: volume and Jones polynomial
• Small volume link orbifolds
• Hyperbolic 3-manifolds of low cusp volume
• Minimal pseudo-Anosov stretch factors on nonoriented surfaces
• Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
• Covolumes of nonuniform lattices in PU(n, 1)
• Two-Generator Free Kleinian Groups and Hyperbolic Displacements
• The Geometry and Arithmetic of Kleinian Groups
• The lowest volume 3-orbifolds with high torsion
• Small optimal Margulis numbers force upper volume bounds
• Generalized Mom-structures and ideal triangulations of 3-manifolds with non-spherical boundary
• On the number of hyperbolic Dehn fillings of a given volume
• Notes on the peripheral volume of hyperbolic 3-manifolds