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Future work:
  • Implement contracting homotopies for the function ResolutionArtinGroup() .
  • Develop more functions for "ZG-resolutions with non-free G-action". Such a resolution R is similar to a free resolution except that it has a component R.stabilizer(e) which returns the stabilizer subgroup Ge in G of each generator e of R. We need to implement a function MakeFree(R) which, using the non-free resolution R and free resolutions Re for each stabilizer group, constructs a free ZG-resolution. The algorithm is explained in [G. Ellis, J. Harris & E. Sköldberg, "Polytopal resolutions for finite groups", J. Reine Angewandte Math., to appear].
  • Apply the function MakeFree(R) in the construction of free ZG-resolutions for: (1) Coxeter groups G which act on the so-called Davis complex; (2) some infinite generalised triangle groups G which act on hyperbolic 3-space;  finite groups G acting faithfully on Euclidean space (this will use Polymake software).

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