Three-manifolds up to complexity
10

Bruno Martelli and I have classified
in [25] and [34]
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 [31] 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