This directory contains the source code and a multitude of
computational details accompanying the paper:
Nathan M Dunfield and Dinakar Ramakrishnan,
Increasing the number of fibered faces of arithmetic hyperbolic 3-manifolds.
In particular, it details the computations in Sections 6, constructing
the target manifold M and checking its various properties.
All files herein are released into the public domain.
Version of Sat Nov 3 12:00:01 2007
Here is a list of the software used:
Magma:
Most of the group theory computations used to construct and
examine the example manifold M.
http://magma.maths.usyd.edu.au/magma/
SnapPeaPython:
Used to actually construct the manifold M and related covers of
the base orbifold B.
http://www.math.uic.edu/~t3m
t3m:
A Python 3-manifold library used to compute the Thurston norm of
M and check whether it fibers.
http://www.math.uic.edu/~t3m
Sage:
Used to piece the Python 3-manifold code together with Magma, and
also for linear algebra over Z used to compute the homology of
certain manifolds. One also needs the optional Sage package
"polymake" for dealing with convex polytopes, as well as having
SnapPeaPython and t3m installed as indicated above.
http://sagemath.org/
Here are the details about each file:
constructing_M.magma:
The Magma code used to construct M, and check the algebraic
properties asserted in Section 6. It is one of the two core files
here.
thurston_norm.py:
Sage/t3m code implementing the trick to compute the Thurston norm
described in Section 6.7 and the fibering test described in
Section 6.11. This is the other core file.
alexander.magma:
Magma code for computing the Alexander polynomial. This is not
specific to our situation, and works for any finitely presented
group.
constructing_M.py:
A very short file of SAGE code which takes the subgroups of
pi_1(B) computed by Magma and uses SnapPeaPython to build the
associated orbifolds.
The remaining files are all SnapPea triangulation files of the various
orbifolds studied.
B, Bfilled :
Two different triangulations of the base orbifold B, discussed in
"constructing_M.magma".
Mraw, Nraw :
The initial triangulations of N and M generated by "constructing_M.py"
Mgood, Ngood:
Other triangulations of M and N which exhibit nice properties with
respect to our approach for computing the Thurston norm and
checking fibering. Used by "thurston_norm.py"
X, Xprime:
Triangulations of X and Xprime, as described in
"constructing_M.magma".