  We apply our previous work on the relation between groupoid homology and
K-theory to Smale spaces. More precisely, we consider the unstable equivalence
relation of a Smale space with totally disconnected stable sets, and prove that
the associated spectral sequence shows Putnam's stable homology groups on the
second sheet. Moreover, this homology is in fact isomorphic to the groupoid
homology of unstable equivalence relation.
