Functorial properties of Putnam’s homology theory for Smale spaces

Abstract

We investigate functorial properties of Putnam’s homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam’s Pullback Lemma from shifts of finite type to non-wandering Smale spaces.