Year: 2009
Type: article
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.
Authors: David Gabai, Robert Meyerhoff, Peter Milley
Institutions: Princeton University, Boston College, The University of Melbourne
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G1332042579, Low Dimensional Topology and Hyperbolic Geometry, FRG: Collaborative Research: Understanding Low-Volume Hyperbolic 3-Manifolds, Three-dimensional geometry and topology, FRG: Collaborative Research: Understanding Low Volume Hyperbolic 3-Manifolds, Invariants of Hyperbolic 3-Manifolds and Applications, FRG: Understanding Low-Volume Hyperbolic 3-Manifolds
OpenAlex ID: W2592234186