English

Minimum-volume hyperbolic 3-manifolds

Geometric Topology 2009-03-13 v3

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.

Keywords

Cite

@article{arxiv.0809.0346,
  title  = {Minimum-volume hyperbolic 3-manifolds},
  author = {Peter Milley},
  journal= {arXiv preprint arXiv:0809.0346},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:15:54.949Z