Topological properties of central tiles for substitutions
Abstract
Central tiles are compact set with fractal boundary that are generated by beta-numeration or substitution numeration systems. They usually generate a self-replicating substitution tiling. Pictures show that there is a large variety of topological properties for these tiles. In this talk, we make use of information on intersections in the self-replicating substitution tiling to deduce sufficient conditions for topological properties, such as connectivity, 0 inner point, homeomorphism to a closed disk and not free fundamental group. These conditions can be checked algorithmically for each given example.