A project to calculate the dimensions of skein modules of mapping tori of T^2, written by Patrick Kinnear.
The formulae are given in a paper of P. Kinnear (arXiv:2304.07332), and this code simply automates the computations. Most code is found in the file skeinslib.sage. The main functions of interest are
get_dim_single_skein
and
get_dim_empty_skein
which take an SL_2(Z)-matrix gamma which defines a mapping torus, and return the dimension of certain direct summands of its Kauffman bracket skein module (for generic q). The total dimension is the sum of the values returned by these functions.
There are additional functions for helping to tabulate, store and display the calculations for conjugacy classes in SL_2(Z). These computations will be published as a github release. The first release, for 3273971 conjugacy classes, was generated on 25th September 2023 by P. Kinnear; further updates will be added as new releases.
Note that the code for writing a nicely-formatted table requires pandas. This can be installed by opening a Sage shell and running
pip install pandas
or by running
sage -pip install pandas
at the command line.
Requirements Sage v9.2 or higher; Python v3.7 or higher.