Functorial properties of Putnam's homology theory for Smale spaces
Deeley, Robin J.
Killough, D. Brady
Whittaker, Michael F.
- Publisher: Cambridge University Press
QA | 37D20 (Primary), 37B10 (Secondary) | Mathematics - Dynamical Systems | Mathematics - K-Theory and Homology
arxiv: Mathematics::Dynamical Systems | Mathematics::Algebraic Topology | Mathematics::Category Theory
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.