Three-manifolds up to complexity
Bruno Martelli and I have classified in  and  the closed, orientable, irreducible 3-manifolds having
Matveev complexity at most 9, i.e. those admitting a triangulation with at most 9 tetrahedra.
Martelli later carried out the same classification in complexity 10.
The complete list of manifolds and a description of their geometry is available.
A computer program that generates the list of manifolds can also be downloaded
(untar the file provided and then read the README file).
Hyperbolic 3-manifolds with boundary
up to complexity 4
Bruno Martelli, Roberto Frigerio and I have classified in  the orientable finite-volume hyperbolic
3-manifolds M with non-empty and compact totally geodesic boundary such that M admits a triangulation
with 3 or 4 but no fewer tetrahedra. The complete list of manifolds in SnapPea format and a description
of their geometric invariants is available.
Page last updated on November 28, 2002