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).
HAP Home
|