Bruno Martelli has created a C++
program based on the notion of o-graph [9]
to manipulate standard spines

(i.e., dually, ideal triangulations)
of 3-manifolds. This program allows to recognize whether two spines are

isomorphic, to modify a spine via
Matveev-Piergallini and disc-replacement moves, and (typically) to

find for any given manifold all the spines
having minimal number of vertices. It also allows to search for the

`bricks' defined in
[25], and it was used to find the data described in
[25], [33], and
[34], and available
here.

(We are hoping to
make a user-frieldly version of the program available from here at
some point.

Actually, we have been hoping
to be able to do this for months, so you should
not expect the program any time soon).

With the help of Roberto Frigerio,
Martelli has also created a program that tests for hyperbolicity

an ideal triangulation of a
candidate hyperbolic 3-manifold with geodesic boundary, computes the volume,

and finds
Kojima's canonical decomposition by randomizing the triangulation and
computing the `tilts'

of the faces. Using this program we have
found all the finite-volume hyperbolic 3-manifolds with

closed non-empty geodesic
boundary and complexity up to 4. The data are described in
[31] and available
here.

The program
itself is eventually available (together with
some explanatory notes).

Page last updated on November 25, 2003