Foliar orientations

To install the "foliar" module into SageMath+SnapPy do the following in this directory:

sage -pip install .

You can test to make sure all is well by doing:

sage -python -m foliar.test

which should conclude with a message such as:

All doctests:
  0 failures out of 73 tests.

Example of searching for a foliar orientation on various triangulations of a closed manifold:

sage: import snappy, foliar
sage: M = snappy.Manifold('m004(1,2)')
sage: eo = foliar.first_foliation(M, 5, 25)
sage: eo.gives_foliation()
True
sage: eo.euler_class_vanishes()
True

Example of searching for a persistently foliar orientation on a 1-cusped manifold:

sage: m004 = snappy.Manifold('m004')
sage: foliar.degeneracy_slopes(m004)
[(1, 0)]
sage: m003 = snappy.Manifold('m003')
sage: foliar.degeneracy_slopes_with_search(m003)
([], [])

Note here that m003 is Floer simple and hence nothing is found.

For many more useful examples, see the docstrings the files "src/main.py" and "src/edge_orient.py".

Data

The file "foliar_tris/persistent_knots.csv.bz2" contains the persistent foliar orientations for some 1.2 million knot exteriors.

Todo

It would not be hard to merge the code here into SnapPy proper, and so this should be done.