Is there any software which can be used for computing Thurston's unit ball (for second homology of 3-manifolds) of link complements? In particular can I do that with SnapPy?

PS: even a table for Thurston's ball of two component links would be helpful for me.

  • $\begingroup$ In principle, the Thurston norm may be computed from Heegaard Floer homology. There are some packages to do this sort of thing, but I have no idea how to use them, or whether they could be modified to compute Thurston norm efficiently. See e.g. math.columbia.edu/~lipshitz/research.html#Programming $\endgroup$
    – Ian Agol
    Sep 29, 2014 at 18:20

2 Answers 2


"Better late than never." Stephan Tillmann and William Worden have produced the software package tnorm. This can be found here:


The software should be able to deal with hyperbolic two-component links easily. William replies to emails, as well. :)


I am not aware of any implementation. The best known algorithm is Cooper and Tillmann's, the closest (which is not very) to a table is in Curt McMullen's classical paper.


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