veering-16 1.0.7

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 into python:

python -m pip install --upgrade veering_16

or into 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. For example, the .identify method now reports that the figure-eight knot complement is the second manifold in the veering census:

>>> 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)]

The figure-eight sibling is the first:

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

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
veer12343(0,0)(0,0)
>>> 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: 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.