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Jan 24, 2012 at 10:02 comment added Tim Porter I have been ferreting around since and have realised that there is more on this if you replace the nerve by the dual Vietoris complex. Then you have a wide range of methods developed for Volodin spaces and Volodin's K-theory. Look back at the papers in the 1970s on higher algebraic K-theory.
Jun 23, 2011 at 10:32 comment added Tim Porter @James These papers: authors me plus... (with R. Brown, and M. Bullejos), Crossed complexes, free crossed resolutions and graph products of groups, in Recent Advances in Group Theory and Low-Dimensional Topology , Research and Exposition in Mathematics vol 27, Helderman Verlag, 2003, pp. 11-26 (with R. Brown, E. Moore and C.D. Wensley), Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups, Georgian Math. J., Special issue for the 70th birthday of H. Inissaridze, 9 (2002) 623 - 644, may be useful as well without involving directly the nerve.
Jun 23, 2011 at 9:52 vote accept James Griffin
Jun 23, 2011 at 9:52 comment added James Griffin Thanks for the reference, their covering is just what I want. You're right that this does deserve to be more widely known. I'll try to find the time to have a proper look at the paper on global actions, I think that I would learn a lot.
Jun 21, 2011 at 6:21 history answered Tim Porter CC BY-SA 3.0