Topology of (some) tiling spaces without finite local complexity

Details Topology of (some) tiling spaces without finite local complexity Topology of (some) tiling spaces without finite local complexity

2007-01-15

arxiv.org/abs/math/0701424v1

Mathematics

Dynamical Systems

21 pages, 5 figures

Scientific paper

A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which tiles can slide past one another. We investigate the topology of a certain class of tiling spaces of this type. We show that they can be written as inverse limits of CW complexes, and their Cech cohomology is related to properties of the fault lines.

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