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Functorial properties of Putnam's homology theory for Smale spaces

Deeley, Robin J.; Killough, D. Brady; Whittaker, Michael F. (2014)
Projects: ARC | Structure and states of operator-algebraic dynamical systems (DP1096001)
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.