http://worldcat.org/entity/work/id/773092616

Topological properties of Rauzy fractals

Rauzy fractals play a major role in many branches of mathematics including number theory, dynamical systems, combinatorics and a theory of quasicrystals. In many problems the topological structure of Rauzy fractals is of crucial importance. This monograph continues a systematic study of topological properties of Rauzy fractals. After a thorough survey on basic results on these fractals, we aim at collective known results on the topology of Rauzy fractals and prove a variety of new ones. We investigate tiling properties, connectivity, homeomorphy to a closed disk as well as the fundamental group of Rauzy fractals. Our main tools are results from plane topology and certain classes of graphs that are defined in terms of tiling properties of Rauzy fractals. We illustrate all our results with many examples.

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