Commentarii Mathematici Helvetici

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Volume 86, Issue 1, 2011, pp. 145–188
DOI: 10.4171/CMH/221

Published online: 2010-12-05

Mom technology and volumes of hyperbolic 3-manifolds

David Gabai[1], Robert Meyerhoff[2] and Peter Milley[3]

(1) Princeton University, USA
(2) Boston College, Chestnut Hill, USA
(3) 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-n manifolds for n ≤ 3, offer a conjectural enumeration when n = 4, and establish important technical results about embedding hyperbolic Mom-n manifolds into hyperbolic 3-manifolds.

Keywords: Mom technology, hyperbolic 3-manifolds, volume

A folder containing programs to help verifiably construct all hyperbolic Mom-2 and Mom-3 manifolds, and to conjecturally construct all hyperbolic Mom-4 manifolds can be downloaded here.

Gabai David, Meyerhoff Robert, Milley Peter: Mom technology and volumes of hyperbolic 3-manifolds. Comment. Math. Helv. 86 (2011), 145-188. doi: 10.4171/CMH/221