Minimum volume cusped hyperbolic three-manifolds

Abstract

This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3 3 -manifolds. Using Mom technology, we prove that any one-cusped hyperbolic 3 3 -manifold with volume ≤ 2.848 \le 2.848 can be obtained by a Dehn filling on one of 21 21 cusped hyperbolic 3 3 -manifolds. We also show how this result can be used to construct a complete list of all one-cusped hyperbolic 3 3 -manifolds with volume ≤ 2.848 \le 2.848 and all closed hyperbolic 3 3 -manifolds with volume ≤ 0.943 \le 0.943 . In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic 3 3 -manifold.