Computer programs for 3-manifolds

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

Page last updated on November 25, 2003