A Comparison of Smale Spaces and Laminations via Inverse Limits

Inverse limits began as a purely topological concept, but have since been applied to areas such as dynamical systems and manifold theory. R.F. Williams related inverse limits to dynamical systems by presenting a construction and realization result relating expanding attractors to inverse limits of branched manifolds. Wieler then adapted these results for Smale Spaces with totally disconnected local stable sets. Rojo used tiling space results to relate inverse limits of branched manifolds to codimension zero laminations. This paper examines the results of Wieler and Rojo and shows that they are analogous