Mom technology and volumes of hyperbolic 3-manifolds

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.