On the cohomology of generalized triangle groups

Graham Ellis, Gerald Williams
2005 Commentarii Mathematici Helvetici  
We describe a general approach to constructing small free Z -resolutions for certain infinite isometry groups . We apply the method to a class of generalized triangle groups and use the resolution to compute the integral homology of these groups. In illustrating the method we also obtain resolutions for the classical triangle groups and for their infinite cyclic central extensions, considered previously by Strebel. (2000) . 20J06, 30F40, 57M60. Mathematics Subject Classification of the
more » ... ion of the integers. The CW-space X can often be constructed as follows. Suppose v ∈ Y is a vector such that the orbit v = {gv | g ∈ } is a discrete subset of Y . The Dirichlet-Voronoi region centred at v is the set
doi:10.4171/cmh/26 fatcat:oaoi2aczm5bcrnbqpcbl2psheu