I'm trying to compute homotopy groups of a few spaces using crossed n-cubes of groups.
I'm able to describe a few colimits in terms of quotients of induced crossed modules and nonabelian tensor products, but even starting with simple groups such as integers and trivial actions it just gets messy really quickly. I have the impression maybe I could turn the description into a computer program to do the heavy lifting, but I admittedly have very little experience with programming, let alone computational group theory.
So my questions are:
Has anyone from computational group theory worked on this problem?
Are there known results along these lines?
What's the best material to read so that I can try to attack this problem my self?