Mom technology and volumes of hyperbolic 3-manifolds

  • David Gabai

    Princeton University, USA
  • Robert Meyerhoff

    Boston College, Chestnut Hill, USA
  • Peter Milley

    Kitchener, Canada


This paper introduces Mom technology to understand low volume hyperbolic 3-manifolds; it is used in [GMM3] and [M1] to show that the Weeks manifold is the unique closed orientable hyperbolic 3-manifold of least volume. Here we enumerate the hyperbolic Mom- manifolds for , offer a conjectural enumeration when , and establish important technical results about embedding hyperbolic Mom- manifolds into hyperbolic 3-manifolds.

Cite this article

David Gabai, Robert Meyerhoff, Peter Milley, Mom technology and volumes of hyperbolic 3-manifolds. Comment. Math. Helv. 86 (2011), no. 1, pp. 145–188

DOI 10.4171/CMH/221