veering-16 1.0.6

Database of veering triangulations up to 16 tetrahedra

This repository contains the manifold database of all transverse veering triangulations with at most sixteen tetrahedra. To install this package, do some version of:

python -m pip install --upgrade veering_16

or, in SageMath:

sage -pip install --upgrade veering_16

To use this module with SnapPy, you need to have SnapPy version 3.3.2 or later. You can check your SnapPy version as follows:

>>> import snappy
>>> snappy.__version__
'3.3.2'

If you have an older version of SnapPy, you can upgrade it as follows:

python -m pip install --upgrade snappy

or, in SageMath:

sage -pip install --upgrade snappy

With the above setup, you can import snappy and then import veering_16 to gain access to the veering census, as follows:

>>> import snappy
>>> import veering_16
>>> M = snappy.Manifold("m004")
>>> M.identify()
[m004(0,0), 4_1(0,0), K2_1(0,0), K4a1(0,0), otet02_00001(0,0), veer1(0,0)]

That is, the figure-eight knot complement is the second manifold in the veering census.

>>> M = snappy.Manifold("veer0")
>>> M.identify()
[m003(0,0), otet02_00000(0,0), veer0(0,0)]

That is, the figure-eight sibling is the first manifold in the veering census. It is possible to slice the veering census in the usual way. For example:

>>> len(snappy.VeeringCensus())
87047
>>> len(snappy.VeeringCensus(num_cusps=1))
59114

Each veering structure consists of a triangulation and an angle structure, as follows.

>>> V = snappy.VeeringCensus()[12343]
>>> V.triangulation_isosig(decorated = False)
'oLAwLwzPQPccbbdfhijkklmnnnhhrhjajxxbbwxxa'
>>> V.angles
'12212201022221'

The triangulation is specified by Burton’s “isosig” format. The angle string describes the taut angle structure (namely, an i in position k means that in tetrahedron k the edge (0,i+1) has dihedral angle pi).

The raw source for the tables are in:

manifold_src/original_manifold_sources

stored as plain text CSV files for the potential convenience of other users. The data is also available from the census webpage.

Andreas Giannopoulos, Saul Schleimer and Henry Segerman. A census of veering structures. https://math.okstate.edu/people/segerman/veering.html, 2019.