LONG EXACT SEQUENCES OF HOMOLOGY GROUPS OF ETALE GROUPOIDS

When a pair of etale groupoids G and G' on totally disconnected spaces are related in some way, we discuss the difference of their homology groups. More specifically, we treat two basic situations. In the subgroupoid situation, G' is assumed to be an open regular subgroupoid of G. In the factor groupoid situation, we assume that G' is a quotient of g and the factor map G -> G' is proper and regular. For each, we show that there exists a long exact sequence of homology groups. We present examples which arise from SFT groupoids and hyperplane groupoids.